Theorem bi2imp

Description: Importation inference similar to imp , except both implications of the hypothesis are biconditionals. (Contributed by Alan Sare, 6-Nov-2017)

	Ref	Expression
Hypothesis	bi2imp.1	⊢ ( 𝜑 ↔ ( 𝜓 ↔ 𝜒 ) )
Assertion	bi2imp	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		bi2imp.1	⊢ ( 𝜑 ↔ ( 𝜓 ↔ 𝜒 ) )
2	1	biimpi	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
3	2	biimpa	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )