Theorem e1a

Description: A Virtual deduction elimination rule. syl is e1a without virtual deductions. (Contributed by Alan Sare, 11-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e1a.1	|- (. ph ->. ps ).
	e1a.2	|- ( ps -> ch )
Assertion	e1a	|- (. ph ->. ch ).

Proof

Step	Hyp	Ref	Expression
1		e1a.1	|- (. ph ->. ps ).
2		e1a.2	|- ( ps -> ch )
3	1	in1	|- ( ph -> ps )
4	3 2	syl	|- ( ph -> ch )
5	4	dfvd1ir	|- (. ph ->. ch ).