Theorem el1

Description: A Virtual deduction elimination rule. syl is el1 without virtual deductions. (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	el1.1	|- (. ph ->. ps ).
	el1.2	|- ( ps -> ch )
Assertion	el1	|- (. ph ->. ch ).

Proof

Step	Hyp	Ref	Expression
1		el1.1	|- (. ph ->. ps ).
2		el1.2	|- ( ps -> ch )
3	1	in1	|- ( ph -> ps )
4	3 2	syl	|- ( ph -> ch )
5	4	dfvd1ir	|- (. ph ->. ch ).