Theorem el021old

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

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

Proof

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