Theorem bi123impib

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

	Ref	Expression
Hypothesis	bi123impib.1	⊢ ( 𝜑 ↔ ( ( 𝜓 ∧ 𝜒 ) ↔ 𝜃 ) )
Assertion	bi123impib	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		bi123impib.1	⊢ ( 𝜑 ↔ ( ( 𝜓 ∧ 𝜒 ) ↔ 𝜃 ) )
2	1	biimpi	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) ↔ 𝜃 ) )
3	2	bi23impib	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )