Metamath Proof Explorer

Theorem trubifal

Description: A <-> identity. (Contributed by Anthony Hart, 22-Oct-2010) (Proof shortened by Andrew Salmon, 13-May-2011) (Proof shortened by Wolf Lammen, 10-Jul-2020)

		Ref	Expression
	Assertion	trubifal	$⊢ (⊤ \leftrightarrow ⊥) \leftrightarrow ⊥$

Proof

Step	Hyp	Ref	Expression
1		bicom	$⊢ (⊤ \leftrightarrow ⊥) \leftrightarrow (⊥ \leftrightarrow ⊤)$
2		falbitru	$⊢ (⊥ \leftrightarrow ⊤) \leftrightarrow ⊥$
3	1 2	bitri	$⊢ (⊤ \leftrightarrow ⊥) \leftrightarrow ⊥$