Theorem bi23imp13

Description: 3imp with middle implication of the hypothesis a biconditional. (Contributed by Alan Sare, 6-Nov-2017)

	Ref	Expression
Hypothesis	bi23imp13.1	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜒 → 𝜃 ) ) )
Assertion	bi23imp13	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

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