Theorem e1bi 42249

Description: Biconditional form of e1a 42247. sylib 217 is e1bi 42249 without virtual deductions. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e1bi.1	⊢ (   𝜑   ▶   𝜓   )
e1bi.2	⊢ (𝜓 ↔ 𝜒)

Assertion

Ref	Expression
e1bi	⊢ (   𝜑   ▶   𝜒   )

Proof of Theorem e1bi

Step	Hyp	Ref	Expression
1		e1bi.1	. 2 ⊢ (   𝜑   ▶   𝜓   )
2		e1bi.2	. . 3 ⊢ (𝜓 ↔ 𝜒)
3	2	biimpi 215	. 2 ⊢ (𝜓 → 𝜒)
4	1, 3	e1a 42247	1 ⊢ (   𝜑   ▶   𝜒   )

Syntax hints:   ↔ wb 205  (   wvd1 42189

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-vd1 42190

This theorem is referenced by:  zfregs2VD  42461  tpid3gVD  42462  en3lplem2VD  42464  ordelordALTVD  42487