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	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	biranri	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		birani.1	⊢ ( 𝜑 ↔ 𝜓 )
2	1	biimpri	⊢ ( 𝜓 → 𝜑 )
3	2	adantr	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜑 )