Theorem el0321old 38942

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

Hypotheses

Ref	Expression
el0321old.1	|- ph
el0321old.2	|- (. (. ps ,. ch ,. th ). ->. ta ).
el0321old.3	|- ( ( ph /\ ta ) -> et )

Assertion

Ref	Expression
el0321old	|- (. (. ps ,. ch ,. th ). ->. et ).

Proof of Theorem el0321old

Step	Hyp	Ref	Expression
1		el0321old.1	. . 3 |- ph
2		el0321old.2	. . . 4 |- (. (. ps ,. ch ,. th ). ->. ta ).
3	2	dfvd3ani 38811	. . 3 |- ( ( ps /\ ch /\ th ) -> ta )
4		el0321old.3	. . 3 |- ( ( ph /\ ta ) -> et )
5	1, 3, 4	eel0321old 38941	. 2 |- ( ( ps /\ ch /\ th ) -> et )
6	5	dfvd3anir 38812	1 |- (. (. ps ,. ch ,. th ). ->. et ).

Syntax hints:   -> wi 4   /\ wa 384   (.wvd1 38785   (.wvhc3 38804

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-vhc3 38805

This theorem is referenced by:  suctrALTcfVD  39159