Theorem e00an 38996

Description: Elimination rule identical to mp2an 708. The non-virtual deduction form is the virtual deduction form, which is mp2an 708. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e00an.1	|- ph
e00an.2	|- ps
e00an.3	|- ( ( ph /\ ps ) -> ch )

Assertion

Ref	Expression
e00an	|- ch

Proof of Theorem e00an

Step	Hyp	Ref	Expression
1		e00an.1	. 2 |- ph
2		e00an.2	. 2 |- ps
3		e00an.3	. 2 |- ( ( ph /\ ps ) -> ch )
4	1, 2, 3	mp2an 708	1 |- ch

Syntax hints:   -> wi 4   /\ wa 384

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 197  df-an 386

This theorem is referenced by: (None)