Theorem el0321old

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

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

Proof

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