Theorem el021old 38926

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
el021old.1	|- ph
el021old.2	|- (. (. ps ,. ch ). ->. th ).
el021old.3	|- ( ( ph /\ th ) -> ta )

Assertion

Ref	Expression
el021old	|- (. (. ps ,. ch ). ->. ta ).

Proof of Theorem el021old

Step	Hyp	Ref	Expression
1		el021old.1	. . 3 |- ph
2		el021old.2	. . . 4 |- (. (. ps ,. ch ). ->. th ).
3	2	dfvd2ani 38799	. . 3 |- ( ( ps /\ ch ) -> th )
4		el021old.3	. . 3 |- ( ( ph /\ th ) -> ta )
5	1, 3, 4	sylancr 695	. 2 |- ( ( ps /\ ch ) -> ta )
6	5	dfvd2anir 38800	1 |- (. (. ps ,. ch ). ->. ta ).

Syntax hints:   -> wi 4   /\ wa 384   (.wvd1 38785   (.wvhc2 38796

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-vhc2 38797

This theorem is referenced by:  sspwimpcfVD  39157  suctrALTcfVD  39159