Theorem e23 38982

Description: A virtual deduction elimination rule (see syl10 79). (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e23.1	|- (. ph ,. ps ->. ch ).
e23.2	|- (. ph ,. ps ,. th ->. ta ).
e23.3	|- ( ch -> ( ta -> et ) )

Assertion

Ref	Expression
e23	|- (. ph ,. ps ,. th ->. et ).

Proof of Theorem e23

Step	Hyp	Ref	Expression
1		e23.1	. . 3 |- (. ph ,. ps ->. ch ).
2	1	vd23 38827	. 2 |- (. ph ,. ps ,. th ->. ch ).
3		e23.2	. 2 |- (. ph ,. ps ,. th ->. ta ).
4		e23.3	. 2 |- ( ch -> ( ta -> et ) )
5	2, 3, 4	e33 38961	1 |- (. ph ,. ps ,. th ->. et ).

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:  e23an  38983  suctrALT2VD  39071  rspsbc2VD  39090  tratrbVD  39097  imbi12VD  39109  imbi13VD  39110