Theorem bi3impa 45467

Description: Similar to 3impa 1127 with implication in hypothesis replaced by biconditional. (Contributed by Alan Sare, 6-Nov-2017.)

Hypothesis

Ref	Expression
bi3impa.1	⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ↔ 𝜃)

Assertion

Ref	Expression
bi3impa	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Proof of Theorem bi3impa

Step	Hyp	Ref	Expression
1		bi3impa.1	. . 3 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ↔ 𝜃)
2	1	biimpi 219	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)
3	2	3impa 1127	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ wa 401   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-3an 1105

This theorem is used by: (None)