## A Christmas Theorem

at 8:01 p.m. on 22. December, 2013

Theorem. Santa Claus exists.

Proof. Let be the sentence "If 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, is of the form where (the antecedent) is just and (the consequent) is "Santa Claus exists." So of course if we assume and show that is true, then we have showed . Hence assume . Hence (by ) Santa Claus exists. But this was the consequent. Hence . Hence Santa Claus exists.

Corollary. Merry Christmas!

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