Theorem e0bir 42350

Description: Elimination rule identical to mpbir 230. The non-virtual deduction form is the virtual deduction form, which is mpbir 230. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e0bir.1	⊢ 𝜑
e0bir.2	⊢ (𝜓 ↔ 𝜑)

Assertion

Ref	Expression
e0bir	⊢ 𝜓

Proof of Theorem e0bir

Step	Hyp	Ref	Expression
1		e0bir.1	. 2 ⊢ 𝜑
2		e0bir.2	. 2 ⊢ (𝜓 ↔ 𝜑)
3	1, 2	mpbir 230	1 ⊢ 𝜓

Syntax hints:   ↔ wb 205

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

This theorem is referenced by: (None)