Theorem e01 31716

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 31622	. 2 |- (. ps ->. ph ).
3		e01.2	. 2 |- (. ps ->. ch ).
4		e01.3	. 2 |- ( ph -> ( ch -> th ) )
5	2, 3, 4	e11 31713	1 |- (. ps ->. th ).

Syntax hints:   -> wi 4   (.wvd1 31585

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 185  df-vd1 31586

This theorem is referenced by:  e01an  31717  trsspwALT  31855  sspwtr  31858  pwtrVD  31863  pwtrrVD  31864  snssiALTVD  31866  snelpwrVD  31870  sstrALT2VD  31873  suctrALT2VD  31875  3impexpVD  31895  ax6e2eqVD  31946  ax6e2ndVD  31947  2sb5ndVD  31949  vk15.4jVD  31953