Theorem e000 38994

Description: A virtual deduction elimination rule. The non-virtual deduction form of e000 38994 is the virtual deduction form. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e000.1	|- ph
e000.2	|- ps
e000.3	|- ch
e000.4	|- ( ph -> ( ps -> ( ch -> th ) ) )

Assertion

Ref	Expression
e000	|- th

Proof of Theorem e000

Step	Hyp	Ref	Expression
1		e000.3	. 2 |- ch
2		e000.1	. . 3 |- ph
3		e000.2	. . 3 |- ps
4		e000.4	. . 3 |- ( ph -> ( ps -> ( ch -> th ) ) )
5	2, 3, 4	mp2 9	. 2 |- ( ch -> th )
6	1, 5	ax-mp 5	1 |- th

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5

This theorem is referenced by:  ax6e2ndeqVD  39145