Theorem e1bir 45612

Description: Right biconditional form of e1a 45609. sylibr 237 is e1bir 45612 without virtual deductions. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e1bir.1	⊢ (   𝜑   ▶   𝜓   )
e1bir.2	⊢ (𝜒 ↔ 𝜓)

Assertion

Ref	Expression
e1bir	⊢ (   𝜑   ▶   𝜒   )

Proof of Theorem e1bir

Step	Hyp	Ref	Expression
1		e1bir.1	. 2 ⊢ (   𝜑   ▶   𝜓   )
2		e1bir.2	. . 3 ⊢ (𝜒 ↔ 𝜓)
3	2	biimpri 231	. 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:  en3lplem2VD  45825