Theorem biranri

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

	Ref	Expression
Hypothesis	birani.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	biranri	$$⊢\left(\psi \wedge \chi \right)\to \phi$$

Proof

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