Theorem e022 38866

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

Hypotheses

Ref	Expression
e022.1	|- ph
e022.2	|- (. ps ,. ch ->. th ).
e022.3	|- (. ps ,. ch ->. ta ).
e022.4	|- ( ph -> ( th -> ( ta -> et ) ) )

Assertion

Ref	Expression
e022	|- (. ps ,. ch ->. et ).

Proof of Theorem e022

Step	Hyp	Ref	Expression
1		e022.1	. . 3 |- ph
2	1	vd02 38823	. 2 |- (. ps ,. ch ->. ph ).
3		e022.2	. 2 |- (. ps ,. ch ->. th ).
4		e022.3	. 2 |- (. ps ,. ch ->. ta ).
5		e022.4	. 2 |- ( ph -> ( th -> ( ta -> et ) ) )
6	2, 3, 4, 5	e222 38861	1 |- (. ps ,. ch ->. et ).

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:  onfrALTVD  39127