Theorem e3bir 45480

Description: Right biconditional form of e3 45478. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e3bir.1	⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
e3bir.2	⊢ (𝜏 ↔ 𝜃)

Assertion

Ref	Expression
e3bir	⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )

Proof of Theorem e3bir

Step	Hyp	Ref	Expression
1		e3bir.1	. 2 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2		e3bir.2	. . 3 ⊢ (𝜏 ↔ 𝜃)
3	2	biimpri 231	. 2 ⊢ (𝜃 → 𝜏)
4	1, 3	e3 45478	1 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )

This proof depends on syntax axioms:   ↔ wb 209  (   wvd3 45329

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-an 402  df-3an 1105  df-vd3 45332

This theorem is used by:  en3lplem2VD  45585