Theorem el12

Description: Virtual deduction form of syl2an . (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	el12.1	|- (. ph ->. ps ).
	el12.2	|- (. ta ->. ch ).
	el12.3	|- ( ( ps /\ ch ) -> th )
Assertion	el12	|- (. (. ph ,. ta ). ->. th ).

Proof

Step	Hyp	Ref	Expression
1		el12.1	|- (. ph ->. ps ).
2		el12.2	|- (. ta ->. ch ).
3		el12.3	|- ( ( ps /\ ch ) -> th )
4	1	in1	|- ( ph -> ps )
5	2	in1	|- ( ta -> ch )
6	4 5 3	syl2an	|- ( ( ph /\ ta ) -> th )
7	6	dfvd2anir	|- (. (. ph ,. ta ). ->. th ).