Metamath Proof Explorer

Theorem truan

Description: True can be removed from a conjunction. (Contributed by FL, 20-Mar-2011) (Proof shortened by Wolf Lammen, 21-Jul-2019)

		Ref	Expression
	Assertion	truan	$⊢ (⊤ \land φ) \leftrightarrow φ$

Step	Hyp	Ref	Expression
1		tru	$⊢ ⊤$
2	1	biantrur	$⊢ φ \leftrightarrow (⊤ \land φ)$
3	2	bicomi	$⊢ (⊤ \land φ) \leftrightarrow φ$