Theorem e0bi 41101

Description: Elimination rule identical to mpbi 232. The non-virtual deduction form is the virtual deduction form, which is mpbi 232. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e0bi.1	⊢ 𝜑
e0bi.2	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
e0bi	⊢ 𝜓

Proof of Theorem e0bi

Step	Hyp	Ref	Expression
1		e0bi.1	. 2 ⊢ 𝜑
2		e0bi.2	. 2 ⊢ (𝜑 ↔ 𝜓)
3	1, 2	mpbi 232	1 ⊢ 𝜓

Syntax hints:   ↔ wb 208

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 209

This theorem is referenced by: (None)