Theorem bi13impib

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

	Ref	Expression
Hypothesis	bi13impib.1	⊢ ( 𝜑 ↔ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) )
Assertion	bi13impib	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		bi13impib.1	⊢ ( 𝜑 ↔ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) )
2	1	biimpi	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) )
3	2	3impib	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )