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Metamath Proof Explorer

Theorem birani

Description: Inference adding a conjunct to the left-hand side of a biconditional. (Contributed by Matthew House, 22-May-2026)

		Ref	Expression
	Hypothesis	birani.1	$⊢ φ \leftrightarrow ψ$
	Assertion	birani	$⊢ (φ \land χ) \to ψ$

Step	Hyp	Ref	Expression
1		birani.1	$⊢ φ \leftrightarrow ψ$
2	1	biimpi	$⊢ φ \to ψ$
3	2	adantr	$⊢ (φ \land χ) \to ψ$