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	$$⊢\phi \leftrightarrow \psi$$
Assertion	birani	$$⊢\left(\phi \wedge \chi \right)\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		birani.1	$$⊢\phi \leftrightarrow \psi$$
2	1	biimpi	$$⊢\phi \to \psi$$
3	2	adantr	$$⊢\left(\phi \wedge \chi \right)\to \psi$$