Theorem bi12imp3

Description: Similar to 3imp except all but innermost implication are biconditionals. (Contributed by Alan Sare, 6-Nov-2017)

	Ref	Expression
Hypothesis	bi12imp3.1	⊢ ( 𝜑 ↔ ( 𝜓 ↔ ( 𝜒 → 𝜃 ) ) )
Assertion	bi12imp3	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		bi12imp3.1	⊢ ( 𝜑 ↔ ( 𝜓 ↔ ( 𝜒 → 𝜃 ) ) )
2	1	biimpi	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜒 → 𝜃 ) ) )
3	2	bi23imp13	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )