Theorem gen11

Description: Virtual deduction generalizing rule for one quantifying variable and one virtual hypothesis. alrimiv is gen11 without virtual deductions. (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	gen11.1	|- (. ph ->. ps ).
Assertion	gen11	|- (. ph ->. A. x ps ).

Proof

Step	Hyp	Ref	Expression
1		gen11.1	|- (. ph ->. ps ).
2		dfvd1imp	|- ( (. ph ->. ps ). -> ( ph -> ps ) )
3	1 2	ax-mp	|- ( ph -> ps )
4	3	alrimiv	|- ( ph -> A. x ps )
5		dfvd1impr	|- ( ( ph -> A. x ps ) -> (. ph ->. A. x ps ). )
6	4 5	ax-mp	|- (. ph ->. A. x ps ).