Then, once this claim ( expressed in the previous sentence ) is proved, it will suffice to prove " φ is either refutable or satisfiable " only for φ's belonging to the class C. Note also that if φ is provably equivalent to ψ ( i. e., ( φ ≡ ψ ) is provable ), then it is indeed the case that " ψ is either refutable or satisfiable " → " φ is either refutable or satisfiable " ( the soundness theorem is needed to show this ).

Then a general definition of isomorphism that covers the previous and many other cases is: an isomorphism is a morphism that has an inverse, i. e. there exists a morphism with and.

Then, five pages later, she quotes the same passage again, but this time in full, straw and all, to show how witches had hallucinations of flight ( Murray 1921, 105-6 ); she does not realise that she has thereby wrecked her previous rationalistic interpretation of the passage.

Then he caught a 23-yard pass from halfback Steve Sewell, becoming the first quarterback ever to catch a pass in the Super Bowl ( Elway had scored a touchdown on that play during opening day the previous year against the Raiders ).

Then general Augereau ( he of the Fructidor-coup ), now commander-in-chief of the French forces in the Netherlands, routinely closed the doors of the Assembly ( by previous arrangement with Pijman ) on September 19, and arrested the dissident Directors.

Then there is the matter that with his previous ties to Theodahad, Boethius apparently found himself on the wrong side in the succession dispute following the untimely death of Eutharic, Theodoric's announced heir.

Then she builds wax cells in which to lay her fertilised eggs from the previous winter.

Then the velocities are substituted for using the previous results.

Then we have only the choice between being nothing in relation to God or having to begin all over again every moment in eternal torment, yet without being able to begin, for if we are able to decide definitely with regard to the previous moment, and so further and further back.

Then in descending order of trim levels were the Caliente, 404 and 202, replacing the previous Custom and base models.

And Then You'll Beg was viewed as being less extreme than Cryptopsy's previous albums.

Then the pistol is again leisurely decocked, and reholstered with an angry brusqueness, which also serves as emphasis for the previous short speech.

Then, the real policemen come and, in an exact match of Bugs ' previous ruse, asks where Rocky and Mugsy are.

Then, a cousin, also named David Ogilvy, claimed the title, suggesting that the previous attainders did not affect its succession, but the House of Lords rejected his claim.

Then the arguments from the previous case are applied to the forces and their components to demonstrate the torque relationships.

Then continue the sequence, where each subsequent term is the sum of the previous n terms.

Then the debaters return to their previous analysis of Pittacus ' and Simonides ' poetry.

Then at one point in the 1960s, Kurokawa and a small group of architects began a new wave of contemporary Japanese architecture, believing that previous solutions and imitations were not satisfactory for the new era: life was not present in Modernism.

Then the verb that belongs to the ‘ wind ’ as subject is not ‘ lay ’, but the previous line of this canto, that says ‘ Thou who didst waken ... And saw ’ ( l. 29, 33 ).

" Hi, Jackie, you're doing fine ," he'd say, " but l've got a little tip for you ..." Then he would mention something he had spotted in my play the previous game.

Then the couple settled back in Greensboro with Mary's daughters from her previous marriage.

Then he loses a huge case against Goffman and slides downhill as previous, disgruntled clients sue him.

Then the current was sampled in eight differential energy-per-charge windows between 50 and 5400 eV at the azimuth where the peak current appeared in the previous series of integral measurements.

Then Define the Great Line was released in which Chamberlain noted that his vocals sounded less like himself imitating Taylor's vocals, and more similar to the vocals of his previous band, This Runs Through.

Then, using the periodic Bernoulli function P < sub > n </ sub > defined above and repeating the argument on the interval, one can obtain an expression of ƒ ( 1 ).

Then the expression of the fine-structure constant becomes the abbreviated

Then, the relativistic expression for the angular distribution of the bremsstrahlung ( considering only the dominant dipole radiation contribution ), is

Then, still black with smoke and with his uniform in shreds, Nelson went on board Victory where he was received on the quarter-deck by Admiral Jervis – " the Admiral embraced me, said he could not sufficiently thank me, and used every kind expression which could not fail to make me happy.

Then combining the last two expression with Beer's law, molar ellipticity becomes:

Then one faces the problem of expression sin ( θ ) and cos ( θ ) as functions of x.

Then, for this expression, one has

Then for each input to that machine, build a Boolean expression which says that the input is passed to the machine, the machine runs correctly, and the machine halts and answers " yes ".

Then the expression can be satisfied if and only if there is a way for the machine to run correctly and answer " yes ", so the satisfiability of the constructed expression is equivalent to asking whether or not the machine will answer " yes ".

Then expression ( 2 ) becomes:

Then figures become more animated in pose and facial expression, tend to be smaller in relation to the background of scenes, and are arranged more freely in the pictorial space, where there is room.

* How to & Then Some: 27 chapters ( 374 pages ) which discuss the full spectrum of sexual expression and its practical aspects, starting from romance and kissing through the different ways people have sex.

Then the general expression of a structural form is, where f is a function, possibly from vectors to vectors in the case of a multiple-equation model.

Then, as Wally leaves the room with a parting bon mot and the canned laughter kicks in, the camera catches June's bewildered, dazed, or amused facial expression.

" Fans find the expression useful, too ... Avoidism: Not originally fannish at all, but a philosophy devised in a rather stomach-turning book, In One Head and Out the Other, this doctrine became confused / associated with the Gandhi-following folk of Eric Frank Russell's " And Then There Were None ".

Then, the set of the Hamiltonian's equations given in the introduction can be expressed in a single expression as

Then, the expression given above for is not the only one that is compatible with such distribution for, and.

Then, unless, then number q has a parent in the Stern – Brocot tree given by the continued fraction expression