Theorem biimpa

Description: Importation inference from a logical equivalence. (Contributed by NM, 3-May-1994)

	Ref	Expression
Hypothesis	biimpa.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
Assertion	biimpa	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		biimpa.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2	1	biimpd	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
3	2	imp	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )