Theorem bi13imp2

Description: Similar to 3imp except the outermost and innermost implications are biconditionals. (Contributed by Alan Sare, 6-Nov-2017)

	Ref	Expression
Hypothesis	bi13imp2.1	⊢ ( 𝜑 ↔ ( 𝜓 → ( 𝜒 ↔ 𝜃 ) ) )
Assertion	bi13imp2	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		bi13imp2.1	⊢ ( 𝜑 ↔ ( 𝜓 → ( 𝜒 ↔ 𝜃 ) ) )
2	1	biimpi	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 ↔ 𝜃 ) ) )
3	2	bi33imp12	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )