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Metamath Proof Explorer

Theorem ibir

Description: Inference that converts a biconditional implied by one of its arguments, into an implication. (Contributed by NM, 22-Jul-2004)

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

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