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Metamath Proof Explorer

Theorem bianir

Description: A closed form of mpbir , analogous to pm2.27 (assertion). (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Roger Witte, 17-Aug-2020)

		Ref	Expression
	Assertion	bianir	$⊢ (φ \land (ψ \leftrightarrow φ)) \to ψ$

Proof

Step	Hyp	Ref	Expression
1		biimpr	$⊢ (ψ \leftrightarrow φ) \to (φ \to ψ)$
2	1	impcom	$⊢ (φ \land (ψ \leftrightarrow φ)) \to ψ$