false is true

Theorem: false is true
Proof:
	Let P be the statement, "If P is true, then false is 	
	true."

	Lemma: P is true.
	Proof: In order to prove the implication of P, we
		assume the premise and try to derive the 
		conclusion.  So assume the premise of P, 
		namely, that P is true.  Since P is true,
		and premise of P, "P is true" is true, then
		we know that the conclusion of P, "false is
		true." is true.  This proves the lemma.

	Now, since P is true, and the premise of P, "P is
	true" is true, the conclusion of P must be true, so 
	therefore false is true.  This concludes the proof.

So what is going on here? Can we easily just prove any arbitrary claim? Of course, this proof contradicts our notion of truth... it can't be that C is true for any statement C. Well, it's as simple as that. Our notion of truth is just not well defined, and leads to contradiction.

Guess we won't be needing that Cause-Effect Nullifier...