Theorem biimparc

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

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

Proof

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