#* Proof: Then so Thus However, is prime, so or In the former case, hence ( which is a contradiction, as neither 1 nor 0 is prime ) or In the latter case, or If however, which is not prime.

#* Proof: suppose that p is composite, hence can be written with a and Then is prime, but and contradicting statement 1.

#* Proof: If q divides 2 < sup > p </ sup > − 1 then 2 < sup > p </ sup > ≡ 1 ( mod q ).

#* Proof: We show if p

#* Based on a line from their first live album " Proof That the Youth Are Revolting " –.

#* We extend this result to more and more complex and lengthy sentences, D < sub > n </ sub > ( n = 1, 2 ...), built out from B, so that either any of them is refutable and therefore so is φ, or all of them are not refutable and therefore each holds in some model.

#* " For as in Adam ALL die, so in Christ ALL will be made alive.

#* " For as in Adam ALL die, so also in Christ shall ALL be made alive " ( ESV ; Emphasis Added )

#* " Consequently, just as the result of one trespass was condemnation for all men, so also the result of one act of righteousness was justification that brings life for all men.

#* " Therefore, as one trespass led to condemnation for all men, so one act of righteousness leads to justification and life for all men.

#* " For God has bound all men over to disobedience so that he may have mercy on them all.

#* After selecting the undesired event and having analyzed the system so that we know all the causing effects ( and if possible their probabilities ) we can now construct the fault tree.

#* If you're just archiving old discussion, use the next available number ; so if the last archive page was Archive 3, call it < tt >< nowiki >/ Archive 4 </ nowiki ></ tt >.

#* The Criminal commits a crime that will not see justice, so the Avenger seeks justice by punishing the Criminal.

#* Snoop: Oh yeah, that's why I have to wear disguise whenever I go out in public so I won't be bothered.

#* The assistance server has a good satellite signal, and plentiful computation power, so it can compare fragmentary signals relayed to it

#* the installation of the Chief Justice of the Irish Supreme Court, who had been legally required to make a declaration of office in front the governor-general, but did not do so on the ( unfounded ) basis that the office had ceased to exist.

#* Ivrit is the language of the Scriptures and so is vital for the study of Judaism

#* " I'm so proud of Van Dyke Parks ' lyrics, and I think the music is inspiring to listen to.

#* Determined to help a girl he likes get her grandfather out of prison ( he ’ s been in prison for two and half years longer than his sentence ), Acerola enlists Laranjinha and a borrowed camcorder from the neighborhood to film his journey from Rio to the capital city of Brasília, all so he can deliver a letter to President Luiz Inacio Lula da Silva.

#* When Laranjinha romances a pretty girl who just so happens to have a boyfriend, he ticks off her jealous beau and has to enlist Acerola for protection.

#* the successor of a natural number is also a natural number, and

#* no natural number is succeeded by " 0 ".

#* An infrared curtain or beam which shines invisible light onto sensors ; if someone or something blocks the beam the door is triggered open.

#* A remote sensor ( e. g. based on infrared or radio waves ) can be triggered by a portable remote control, or is installed inside a vehicle.

#* Second Council of Ephesus ( 449 ) declared Eutyches orthodox and attacked his opponents. Though originally convened as an ecumenical council, this council is not recognized as ecumenical and denounced as a Robber Council by the Chalcedonians ( Catholics, Eastern Orthodox, Protestants ).

#* This is done by first noting that a sentence such as is either refutable or has some model in which it holds ; this model is simply assigning truth values to the subpropositions from which B is built.

#* The answer is " agree.

#* The answer is " energy.

#* The answer is " say.

#* The answer is the three-word sentence " I am hungry.

#* The answer is " angry " and " hungry.

#* The answer is " every ," and the logic is as follows: There are three words, ending " g ," " r ," and " y.

#* The answer to this version is " language " -- the third word in the phrase " the English language.

#* The answer is " what.

#* The answer is " three ," the third word in the paragraph.

#* The answer is the word " one ," which is the third " one.

#* place a piece from the reserve on an empty square on the board

#* move a previously placed piece to an empty square

#* move a piece to a square occupied by an opposing piece, capturing it.

#* Then swap the new root with the root on the heap to the left ( this will not disturb the heap property of the current heap ).

#* While the current heap has a size greater than 1 and either child heap of the current heap has a root node greater than the root of the current heap

#* of the basic root вѣт-,

#* If this is the root node ( which thus has no parent ):

#* Hormonal root pruning theory-in the new theory just like ethylene, GA / BA are seen both to be induced by sugar and gas shortages in the roots, and to push sugar and gases, as well as minerals, water and the growth hormones out of the root cell causing a positive feedback loop resulting the emptying and death of the root cell.