Theorem e1bi 45611

Description: Biconditional form of e1a 45609. sylib 221 is e1bi 45611 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 219	. 2 ⊢ (𝜓 → 𝜒)
4	1, 3	e1a 45609	1 ⊢ (   𝜑   ▶   𝜒   )

This proof depends on syntax axioms:   ↔ wb 209  (   wvd1 45551

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-vd1 45552

This theorem is used by:  zfregs2VD  45822  tpid3gVD  45823  en3lplem2VD  45825  ordelordALTVD  45848