Theorem bi3impb 41992

Description: Similar to 3impb 1113 with implication in hypothesis replaced by biconditional. (Contributed by Alan Sare, 6-Nov-2017.)

Hypothesis

Ref	Expression
bi3impb.1	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) ↔ 𝜃)

Assertion

Ref	Expression
bi3impb	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Proof of Theorem bi3impb

Step	Hyp	Ref	Expression
1		bi3impb.1	. . 3 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) ↔ 𝜃)
2	1	biimpi 215	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	2	3impb 1113	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ↔ wb 205   ∧ wa 395   ∧ w3a 1085

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 396  df-3an 1087

This theorem is referenced by: (None)