Theorem bi23imp1

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

	Ref	Expression
Hypothesis	bi23imp1.1	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜒 ↔ 𝜃 ) ) )
Assertion	bi23imp1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		bi23imp1.1	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜒 ↔ 𝜃 ) ) )
2		biimp	⊢ ( ( 𝜒 ↔ 𝜃 ) → ( 𝜒 → 𝜃 ) )
3	1 2	syl6bi	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
4	3	3imp	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )