Theorem e010 38909

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e010.1	|- ph
e010.2	|- (. ps ->. ch ).
e010.3	|- th
e010.4	|- ( ph -> ( ch -> ( th -> ta ) ) )

Assertion

Ref	Expression
e010	|- (. ps ->. ta ).

Proof of Theorem e010

Step	Hyp	Ref	Expression
1		e010.1	. . 3 |- ph
2	1	vd01 38822	. 2 |- (. ps ->. ph ).
3		e010.2	. 2 |- (. ps ->. ch ).
4		e010.3	. . 3 |- th
5	4	vd01 38822	. 2 |- (. ps ->. th ).
6		e010.4	. 2 |- ( ph -> ( ch -> ( th -> ta ) ) )
7	2, 3, 5, 6	e111 38899	1 |- (. ps ->. ta ).

Syntax hints:   -> wi 4   (.wvd1 38785

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-vd1 38786

This theorem is referenced by: (None)