Theorem bi23impib

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

	Ref	Expression
Hypothesis	bi23impib.1	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) ↔ 𝜃 ) )
Assertion	bi23impib	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		bi23impib.1	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) ↔ 𝜃 ) )
2	1	biimpd	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) )
3	2	3impib	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )