Theorem e012 38892

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

Hypotheses

Ref	Expression
e012.1	|- ph
e012.2	|- (. ps ->. ch ).
e012.3	|- (. ps ,. th ->. ta ).
e012.4	|- ( ph -> ( ch -> ( ta -> et ) ) )

Assertion

Ref	Expression
e012	|- (. ps ,. th ->. et ).

Proof of Theorem e012

Step	Hyp	Ref	Expression
1		e012.1	. . 3 |- ph
2	1	vd01 38822	. 2 |- (. ps ->. ph ).
3		e012.2	. 2 |- (. ps ->. ch ).
4		e012.3	. 2 |- (. ps ,. th ->. ta ).
5		e012.4	. 2 |- ( ph -> ( ch -> ( ta -> et ) ) )
6	2, 3, 4, 5	e112 38879	1 |- (. ps ,. th ->. et ).

Syntax hints:   -> wi 4   (.wvd1 38785   (.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-vd1 38786  df-vd2 38794

This theorem is referenced by: (None)