Theorem gen11nv

Description: Virtual deduction generalizing rule for one quantifying variable and one virtual hypothesis without distinct variables. alrimih is gen11nv without virtual deductions. (Contributed by Alan Sare, 12-Dec-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	gen11nv.1	|- ( ph -> A. x ph )
	gen11nv.2	|- (. ph ->. ps ).
Assertion	gen11nv	|- (. ph ->. A. x ps ).

Proof

Step	Hyp	Ref	Expression
1		gen11nv.1	|- ( ph -> A. x ph )
2		gen11nv.2	|- (. ph ->. ps ).
3	2	in1	|- ( ph -> ps )
4	1 3	alrimih	|- ( ph -> A. x ps )
5	4	dfvd1ir	|- (. ph ->. A. x ps ).