Theorem bi1imp

Description: Importation inference similar to imp , except the outermost implication of the hypothesis is a biconditional. (Contributed by Alan Sare, 6-Nov-2017)

	Ref	Expression
Hypothesis	bi1imp.1	⊢ ( 𝜑 ↔ ( 𝜓 → 𝜒 ) )
Assertion	bi1imp	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		bi1imp.1	⊢ ( 𝜑 ↔ ( 𝜓 → 𝜒 ) )
2	1	biimpi	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
3	2	imp	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )