Theorem e233 38992

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 29-Feb-2012.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e233.1	|- (. ph ,. ps ->. ch ).
e233.2	|- (. ph ,. ps ,. th ->. ta ).
e233.3	|- (. ph ,. ps ,. th ->. et ).
e233.4	|- ( ch -> ( ta -> ( et -> ze ) ) )

Assertion

Ref	Expression
e233	|- (. ph ,. ps ,. th ->. ze ).

Proof of Theorem e233

Step	Hyp	Ref	Expression
1		e233.1	. . . 4 |- (. ph ,. ps ->. ch ).
2	1	dfvd2i 38801	. . 3 |- ( ph -> ( ps -> ch ) )
3		e233.2	. . . 4 |- (. ph ,. ps ,. th ->. ta ).
4	3	dfvd3i 38808	. . 3 |- ( ph -> ( ps -> ( th -> ta ) ) )
5		e233.3	. . . 4 |- (. ph ,. ps ,. th ->. et ).
6	5	dfvd3i 38808	. . 3 |- ( ph -> ( ps -> ( th -> et ) ) )
7		e233.4	. . 3 |- ( ch -> ( ta -> ( et -> ze ) ) )
8	2, 4, 6, 7	ee233 38725	. 2 |- ( ph -> ( ps -> ( th -> ze ) ) )
9	8	dfvd3ir 38809	1 |- (. ph ,. ps ,. th ->. ze ).

Syntax hints:   -> wi 4   (.wvd2 38793   (.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-vd2 38794  df-vd3 38806

This theorem is referenced by:  truniALTVD  39114  onfrALTlem2VD  39125