Theorem e121 38881

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

Hypotheses

Ref	Expression
e121.1	|- (. ph ->. ps ).
e121.2	|- (. ph ,. ch ->. th ).
e121.3	|- (. ph ->. ta ).
e121.4	|- ( ps -> ( th -> ( ta -> et ) ) )

Assertion

Ref	Expression
e121	|- (. ph ,. ch ->. et ).

Proof of Theorem e121

Step	Hyp	Ref	Expression
1		e121.1	. . 3 |- (. ph ->. ps ).
2	1	vd12 38825	. 2 |- (. ph ,. ch ->. ps ).
3		e121.2	. 2 |- (. ph ,. ch ->. th ).
4		e121.3	. . 3 |- (. ph ->. ta ).
5	4	vd12 38825	. 2 |- (. ph ,. ch ->. ta ).
6		e121.4	. 2 |- ( ps -> ( th -> ( ta -> et ) ) )
7	2, 3, 5, 6	e222 38861	1 |- (. ph ,. ch ->. 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:  e021  38890  tratrbVD  39097