Metamath Proof Explorer

Theorem trunanfal

Description: A -/\ identity. (Contributed by Anthony Hart, 23-Oct-2010) (Proof shortened by Andrew Salmon, 13-May-2011) (Proof shortened by Wolf Lammen, 10-Jul-2020)

		Ref	Expression
	Assertion	trunanfal	$⊢ (⊤ ⊼ ⊥) \leftrightarrow ⊤$

Proof

Step	Hyp	Ref	Expression
1		df-nan	$⊢ (⊤ ⊼ ⊥) \leftrightarrow \neg (⊤ \land ⊥)$
2		truanfal	$⊢ (⊤ \land ⊥) \leftrightarrow ⊥$
3	1 2	xchbinx	$⊢ (⊤ ⊼ ⊥) \leftrightarrow \neg ⊥$
4		notfal	$⊢ \neg ⊥ \leftrightarrow ⊤$
5	3 4	bitri	$⊢ (⊤ ⊼ ⊥) \leftrightarrow ⊤$