Theorem bi13imp23

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

	Ref	Expression
Hypothesis	bi13imp23.1	⊢ ( 𝜑 ↔ ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
Assertion	bi13imp23	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		bi13imp23.1	⊢ ( 𝜑 ↔ ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2	1	biimpi	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
3	2	3imp	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )