Theorem biimpac

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

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

Proof

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