Theorem bi13impia

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

	Ref	Expression
Hypothesis	bi13impia.1	⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜒 → 𝜃 ) )
Assertion	bi13impia	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		bi13impia.1	⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜒 → 𝜃 ) )
2	1	biimpi	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) )
3	2	3impia	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )