Metamath Proof Explorer


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 ).