(1) If C is true, then If C is true, then Santa Claus exists.Or, to spell it out,
(1') If if C is true, then Santa Claus exists is true, then (if C is true, then Santa Claus exists).Note that the parenthetical antecedent is true when C is true (after all, that's what C means), so (1) pretty clearly entails by modus ponens,
(2) If if C is true, then Santa Claus exists is true, then Santa Claus exists.But since the italic claim in (2) above just is C, (2) is pretty clearly also equivalent to C. So let's sub it in:
(3) If C is true, then Santa Claus exists.(3), of course, is equivalent to C. So it follows from modus ponens on (3) and (3),
(4) Santa Claus exists.Of course, you should feel free to sub in your favorite implausible claim for "Santa Claus exists". This argument would be equally effective at proving that God exists, or that the St. Louis Rams are worthy of praise. There's a lot of big logic-y words in my explanation, but it's actually all very intuitive... if talk of modus ponens and equivalence and entailment makes your eyes glaze over, then just look at the numbered sentences -- you should be able to see that they follow logically from one another. UPDATE 11/21: I had no idea that "Santa Claus" didn't have an "e" in it. How very, very strange.