Theorem e3bi 42358

Description: Biconditional form of e3 42357. syl8ib 255 is e3bi 42358 without virtual deductions. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e3bi.1	⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
e3bi.2	⊢ (𝜃 ↔ 𝜏)

Assertion

Ref	Expression
e3bi	⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )

Proof of Theorem e3bi

Step	Hyp	Ref	Expression
1		e3bi.1	. 2 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2		e3bi.2	. . 3 ⊢ (𝜃 ↔ 𝜏)
3	2	biimpi 215	. 2 ⊢ (𝜃 → 𝜏)
4	1, 3	e3 42357	1 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )

Syntax hints:   ↔ wb 205  (   wvd3 42207

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 397  df-3an 1088  df-vd3 42210

This theorem is referenced by:  en3lplem2VD  42464