Theorem e02 38922

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e02.1	|- ph
e02.2	|- (. ps ,. ch ->. th ).
e02.3	|- ( ph -> ( th -> ta ) )

Assertion

Ref	Expression
e02	|- (. ps ,. ch ->. ta ).

Proof of Theorem e02

Step	Hyp	Ref	Expression
1		e02.1	. . 3 |- ph
2	1	vd02 38823	. 2 |- (. ps ,. ch ->. ph ).
3		e02.2	. 2 |- (. ps ,. ch ->. th ).
4		e02.3	. 2 |- ( ph -> ( th -> ta ) )
5	2, 3, 4	e22 38896	1 |- (. ps ,. ch ->. ta ).

Syntax hints:   -> wi 4   (.wvd2 38793

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  df-vd2 38794

This theorem is referenced by:  e02an  38923  onfrALTlem3VD  39123  vk15.4jVD  39150