Theorem bi123impia

Description: 3impia with the implications of the hypothesis biconditionals. (Contributed by Alan Sare, 6-Nov-2017)

	Ref	Expression
Hypothesis	bi123impia.1	⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜒 ↔ 𝜃 ) )
Assertion	bi123impia	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		bi123impia.1	⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜒 ↔ 𝜃 ) )
2	1	biimpi	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 ↔ 𝜃 ) )
3	2	biimp3a	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )