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Metamath Proof Explorer

Theorem ibi

Description: Inference that converts a biconditional implied by one of its arguments, into an implication. (Contributed by NM, 17-Oct-2003)

		Ref	Expression
	Hypothesis	ibi.1	$⊢ φ \to (φ \leftrightarrow ψ)$
	Assertion	ibi	$⊢ φ \to ψ$

Step	Hyp	Ref	Expression
1		ibi.1	$⊢ φ \to (φ \leftrightarrow ψ)$
2		id	$⊢ φ \to φ$
3	2 1	mpbid	$⊢ φ \to ψ$