Theorem gen11nv 38842

Description: Virtual deduction generalizing rule for one quantifying variable and one virtual hypothesis without distinct variables. alrimih 1751 is gen11nv 38842 without virtual deductions. (Contributed by Alan Sare, 12-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
gen11nv	|- (. ph ->. A. x ps ).

Proof of Theorem gen11nv

Step	Hyp	Ref	Expression
1		gen11nv.1	. . 3 |- ( ph -> A. x ph )
2		gen11nv.2	. . . 4 |- (. ph ->. ps ).
3	2	in1 38787	. . 3 |- ( ph -> ps )
4	1, 3	alrimih 1751	. 2 |- ( ph -> A. x ps )
5	4	dfvd1ir 38789	1 |- (. ph ->. A. x ps ).

Syntax hints:   -> wi 4   A.wal 1481   (.wvd1 38785

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-vd1 38786

This theorem is referenced by:  tratrbVD  39097  hbimpgVD  39140  hbalgVD  39141  hbexgVD  39142  e2ebindVD  39148