Metamath Proof Explorer

Theorem fal

Description: The truth value F. is refutable. (Contributed by Anthony Hart, 22-Oct-2010) (Proof shortened by Mel L. O'Cat, 11-Mar-2012)

		Ref	Expression
	Assertion	fal	$⊢ \neg ⊥$

Step	Hyp	Ref	Expression
1		tru	$⊢ ⊤$
2	1	notnoti	$⊢ \neg \neg ⊤$
3		df-fal	$⊢ ⊥ \leftrightarrow \neg ⊤$
4	2 3	mtbir	$⊢ \neg ⊥$