Theorem e01 37138

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e01.1	|- ph
e01.2	|- (. ps ->. ch ).
e01.3	|- ( ph -> ( ch -> th ) )

Assertion

Ref	Expression
e01	|- (. ps ->. th ).

Proof of Theorem e01

Step	Hyp	Ref	Expression
1		e01.1	. . 3 |- ph
2	1	vd01 37044	. 2 |- (. ps ->. ph ).
3		e01.2	. 2 |- (. ps ->. ch ).
4		e01.3	. 2 |- ( ph -> ( ch -> th ) )
5	2, 3, 4	e11 37135	1 |- (. ps ->. th ).

Syntax hints:   -> wi 4   (.wvd1 37007

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 190  df-vd1 37008

This theorem is referenced by:  e01an  37139  trsspwALT  37269  sspwtr  37272  pwtrVD  37283  pwtrrVD  37284  snssiALTVD  37286  snelpwrVD  37290  sstrALT2VD  37293  suctrALT2VD  37295  3impexpVD  37315  ax6e2eqVD  37367  ax6e2ndVD  37368  2sb5ndVD  37370  vk15.4jVD  37374