Theorem e13 38975

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

Hypotheses

Ref	Expression
e13.1	|- (. ph ->. ps ).
e13.2	|- (. ph ,. ch ,. th ->. ta ).
e13.3	|- ( ps -> ( ta -> et ) )

Assertion

Ref	Expression
e13	|- (. ph ,. ch ,. th ->. et ).

Proof of Theorem e13

Step	Hyp	Ref	Expression
1		e13.1	. . 3 |- (. ph ->. ps ).
2	1	vd13 38826	. 2 |- (. ph ,. ch ,. th ->. ps ).
3		e13.2	. 2 |- (. ph ,. ch ,. th ->. ta ).
4		e13.3	. 2 |- ( ps -> ( ta -> et ) )
5	2, 3, 4	e33 38961	1 |- (. ph ,. ch ,. th ->. 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:  e13an  38976  en3lplem2VD  39079  rspsbc2VD  39090  ssralv2VD  39102  imbi12VD  39109  imbi13VD  39110  truniALTVD  39114