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Metamath Proof Explorer

Theorem anidmdbi

Description: Conjunction idempotence with antecedent. (Contributed by Roy F. Longton, 8-Aug-2005)

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

Step	Hyp	Ref	Expression
1		anidm	$⊢ (ψ \land ψ) \leftrightarrow ψ$
2	1	imbi2i	$⊢ (φ \to (ψ \land ψ)) \leftrightarrow (φ \to ψ)$