Theorem el123

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

	Ref	Expression
Hypotheses	el123.1	|- (. ph ->. ps ).
	el123.2	|- (. ch ->. th ).
	el123.3	|- (. ta ->. et ).
	el123.4	|- ( ( ps /\ th /\ et ) -> ze )
Assertion	el123	|- (. (. ph ,. ch ,. ta ). ->. ze ).

Proof

Step	Hyp	Ref	Expression
1		el123.1	|- (. ph ->. ps ).
2		el123.2	|- (. ch ->. th ).
3		el123.3	|- (. ta ->. et ).
4		el123.4	|- ( ( ps /\ th /\ et ) -> ze )
5	1	in1	|- ( ph -> ps )
6	2	in1	|- ( ch -> th )
7	3	in1	|- ( ta -> et )
8	5 6 7 4	syl3an	|- ( ( ph /\ ch /\ ta ) -> ze )
9	8	dfvd3anir	|- (. (. ph ,. ch ,. ta ). ->. ze ).