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A Christmas Theorem

22. December, 2013

Theorem. Santa Claus exists.

Proof. Let S be the sentence "If S then Santa Claus exists." This looks a bit self-referential but actually such a sentence, or an equivalent one, is constructible by the Diagonalisation Lemma.

Now, S is of the form P\implies Q where P (the antecedent) is just S and Q (the consequent) is "Santa Claus exists." So of course if we assume P and show that Q is true, then we have showed P\implies Q. Hence assume S. Hence (by S) Santa Claus exists. But this was the consequent. Hence S. Hence Santa Claus exists. \qed

Corollary. Merry Christmas!