Theorem e31 38978

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e31.1	|- (. ph ,. ps ,. ch ->. th ).
e31.2	|- (. ph ->. ta ).
e31.3	|- ( th -> ( ta -> et ) )

Assertion

Ref	Expression
e31	|- (. ph ,. ps ,. ch ->. et ).

Proof of Theorem e31

Step	Hyp	Ref	Expression
1		e31.1	. 2 |- (. ph ,. ps ,. ch ->. th ).
2		e31.2	. . 3 |- (. ph ->. ta ).
3	2	vd13 38826	. 2 |- (. ph ,. ps ,. ch ->. ta ).
4		e31.3	. 2 |- ( th -> ( ta -> et ) )
5	1, 3, 4	e33 38961	1 |- (. ph ,. ps ,. ch ->. et ).

Syntax hints:   -> wi 4   (.wvd1 38785   (.wvd3 38803

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-3an 1039  df-vd1 38786  df-vd3 38806

This theorem is referenced by:  e31an  38980  trintALTVD  39116