Let A be the sentence "If A is true, then Santa Claus exists".
Suppose that A is true, that is, suppose that if A is true then Santa
Claus exists. Then, since A is true, Santa Claus exists. Thus, we
have shown that *if* A is true, then Santa Claus exists. But that is
precisely the sentence A. Hence, A is true. Hence, Santa Claus
exists.