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Every formula in classical logic is equivalent to a formula in prenex normal form.

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## Some Related Sentences

Every and formula

* ( Completeness )

__Every__universally valid second-order__formula__, under standard semantics,**is**provable**.**__Every__first-order

__formula__

**is**logically

**equivalent**(

**in**

**classical**

**logic**)

**to**some

__formula__

**in**

**prenex**

**normal**

**form**

**.**

__Every__first-order

__formula__can be converted into Skolem

**normal**

**form**while not changing its satisfiability via

**a**process called Skolemization ( sometimes spelled " Skolemnization ").

A substructure N of M

**is**elementary if and only if it passes the Tarski – Vaught test:__Every__first-order__formula__φ ( x, b < sub > 1 </ sub >, …, b < sub > n </ sub >) with parameters**in**N that has**a**solution**in**M also has**a**solution**in**N when evaluated**in**M**.**One can prove that two structures are elementary**equivalent**with the Ehrenfeucht – Fraïssé games**.**__Every__once

**in**

**a**while, the column steered away from its usual

__formula__

**to**feature an issue that was

**a**current widespread issue

**.**

__Every__arithmetical set

**is**implicitly arithmetical ; if X

**is**arithmetically defined by φ ( n ) then it

**is**implicitly defined by the

__formula__

Every and classical

__Every__argues that " the disparagement of myth

**in**our own civilization " stems partly from objections

**to**perceived idolatry, objections which intensified

**in**the Reformation, both among Protestants and among Catholics reacting against the

__classical__mythology revived during the Renaissance

**.**

__Every__year he exhibited work of one class or another: occasionally

**a**public monument

**in**the round, like those of Pasquale Paoli ( 1798 ) or Captain Montague ( 1802 ) for Westminster Abbey, of Sir William Jones for University College, Oxford ( 1797 – 1801 ), of Nelson or Howe for St Paul's Cathedral ; more often memorials for churches, with symbolic Acts of Mercy or illustrations of Scripture texts, both commonly

**in**low relief ( 1801 ), Miss Cromwell, Chichester ( 1800 ), Mrs Knight, Milton, Cambridge ( 1802 ), and many more ; and these pious labours he would vary from time

**to**time with

**a**

__classical__piece like those of his earliest predilection

**.**

__Every__single step

**in**

__classical__ballet

**is**performed with hips, knees and feet as turned out as possible, except when otherwise specified by choreography

**.**

__Every__autumn, according

**to**Plutarch ( Life of Lycurgus, 28, 3 – 7 ), the Spartan ephors (

__classical__Greek ) would pro forma declare war on the helot population so that any Spartan citizen could kill

**a**helot without fear of blood guilt

**.**

__Every__

__classical__theorem that applies

**to**the natural numbers applies

**to**the non-standard natural numbers

**.**

Every and logic

__Every__Boolean algebra ( A, ∧, ∨) gives rise

**to**

**a**ring ( A, +, ·) by defining

**a**+ b := (

**a**∧ ¬ b ) ∨ ( b ∧ ¬

**a**) = (

**a**∨ b ) ∧ ¬(

**a**∧ b ) ( this operation

**is**called symmetric difference

**in**the case of sets and XOR

**in**the case of

__logic__) and

**a**· b :=

**a**∧ b

**.**The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring

**is**the 1 of the Boolean algebra

**.**

__Every__facet of Cartoon Action Hour was created with an eye toward faithfully depicting the subject matter, using what the authors refer

**to**as " cartoon

__logic__".

__Every__game object

**is**defined by its appearance ( graphics, animations, captions, fonts ) and by

**a**script, which defines the underlying

__logic__of

**a**given game object and its responses

**to**game events

**.**

Every and is

__Every__legislator from Brasstown Bald

**to**Folkston

__is__going

**to**have his every vote subjected

**to**the closest scrutiny as

**a**test of his political allegiances, not his convictions

**.**

__Every__detail

**in**his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings

**to**the fifth variation ( an obvious indication that he

__is__playing with Viennese musicians ), and the gossamer shading throughout

**.**

__Every__taxpayer

__is__well aware of the vast size of our annual defense budget and most of our readers also realize that

**a**large portion of these expenditures go for military electronics

**.**

__Every__few days,

**in**the early morning, as the work progressed, twenty men would appear

**to**push it ahead and

**to**shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it

__is__by ancient brick vaulting

**.**

__Every__dream, and this

__is__true of

**a**mental image of any type even though it may be readily interpreted into its

**equivalent**of wakeful thought,

__is__

**a**psychic phenomenon for which no explanation

__is__available

**.**

__Every__library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it

__is__

**to**hear the librarian say apologetically, `` I'm sorry, but we don't have that book

**.**

__Every__community, if it

__is__alive has

**a**spirit, and that spirit

__is__the center of its unity and identity

**.**

The restricted principle "

__Every__partially ordered set has**a**maximal totally ordered subset "__is__also**equivalent****to**AC over ZF**.**__Every__natural-born citizen of

**a**foreign state who

__is__also an American citizen and every natural-born American citizen who

__is__

**a**citizen of

**a**foreign land owes

**a**double allegiance, one

**to**the United States, and one

**to**his homeland (

**in**the event of an immigrant becoming

**a**citizen of the US ), or

**to**his adopted land (

**in**the event of an emigrant natural born citizen of the US becoming

**a**citizen of another nation ).

__Every__line of written text

__is__

**a**mere reflection of references from any of

**a**multitude of traditions, or, as Barthes puts it, " the text

__is__

**a**tissue of quotations drawn from the innumerable centres of culture "; it

__is__never original

**.**

__Every__year, on the last Sunday

**in**April, there

__is__an ice fishing competition

**in**the frozen estuarine waters of the Anadyr River's mouth

**.**

__Every__lattice element of the structure

__is__

**in**its proper place, whether it

__is__

**a**single atom or

**a**molecular grouping

**.**

Every and equivalent

*

__Every__quadratic Bézier curve**is**also**a**cubic Bézier curve, and more generally, every degree n Bézier curve**is**also**a**degree m curve for any m > n**.**In detail,**a**degree n curve with control points P < sub > 0 </ sub >, …, P < sub > n </ sub >**is**__equivalent__( including the parametrization )**to**the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where**.**__Every__context-sensitive grammar which does not generate the empty string can be transformed into an

__equivalent__one

**in**Kuroda

**normal**

**form**

**.**

__Every__grammar

**in**Chomsky

**normal**

**form**

**is**context-free, and conversely, every context-free grammar can be transformed into an

__equivalent__one which

**is**

**in**Chomsky

**normal**

**form**

**.**

__Every__question and method about differential equations has

**a**discrete

__equivalent__for difference equations

**.**

__Every__Dean of the Faculty (

__equivalent__

**to**

**a**Provost at most universities ) has always been an active-duty brigadier general, although technically,

**a**civilian may hold the position

**.**

__Every__homeomorphism

**is**

**a**homotopy equivalence, but the converse

**is**not true: for example,

**a**solid disk

**is**not homeomorphic

**to**

**a**single point, although the disk and the point are homotopy

__equivalent__

**.**

__Every__quadratic

**form**q

**in**n variables over

**a**field of characteristic not equal

**to**2

**is**

__equivalent__

**to**

**a**diagonal

**form**

__Every__Riemann surface

**is**the quotient of

**a**free, proper and holomorphic action of

**a**discrete group on its universal covering and this universal covering

**is**holomorphically isomorphic ( one also says: " conformally

__equivalent__")

**to**one of the following:

__Every__year on the

__equivalent__date

**to**the 23rd of March on the Chinese Calendar, the birthday of Mazu

**is**commemorated with concerts, lion dance, Carrying god ride ' Kheng kiu ', ' siam hee ' and also wayang kulit show for three days

**.**

__Every__year,

**a**volume of over 2 million forty-foot

__equivalent__units ( FEU )

**is**transported worldwide

**.**

__Every__year during this period, more than

**a**hundred MBA students from IIM Calcutta leave for foreign institutes, and an

__equivalent__number from various B-schools arrive

**in**IIM Calcutta

**to**spend the term there

**.**

__Every__CW-complex possesses

**a**Postnikov tower, that

**is**, it

**is**homotopy

__equivalent__

**to**an iterated fibration with fibers the Eilenberg – MacLane spaces

**.**

__Every__man had

**to**go

**to**church once

**a**week or be fined 12 pence (

__equivalent__

**to**just over £ 11

**in**2007 ),

**a**considerable sum for the poor

**.**

__Every__Toontask has an award for completion, such as additional " laff points " (

__equivalent__

**to**the player's " health "), jellybeans ( the in-game currency ), and

**a**variety of other benefits

**.**

*

__Every__time**a**loan balance**is**reduced, an__equivalent__number of bonds are identified by lottery and converted into**a**different bond also with**a**one cent par value ( that will convert at par into cash at the next payment date ).0.839 seconds.