### Santa Exists

Of course there are loads of interesting ways of generating a contradiction and using it to prove something humorously false, but I thought this one was worth copying.

Let S be the sentence, "If S is true, Santa exists".

1. Assume S is true.

Then, substituting for S, and by assumption:

2. "If S is true, Santa exists" is true.

So, by our assumption:

3. Santa exists

From only the assumption 1, we have reached 3, so we may conclude (without assumption):

4. If S is true, Santa exists.

So we have shown 4 is true, thus

5. "If S is true, Santa exists" is true.

Hence

6. S is true.

Using 4 and 6, we reach:

7. Santa exists.