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Theorem gen11nv 36996
Description: Virtual deduction generalizing rule for one quantifying variable and one virtual hypothesis without distinct variables. alrimih 1693 is gen11nv 36996 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
StepHypRef Expression
1 gen11nv.1 . . 3  |-  ( ph  ->  A. x ph )
2 gen11nv.2 . . . 4  |-  (. ph  ->.  ps
).
32in1 36941 . . 3  |-  ( ph  ->  ps )
41, 3alrimih 1693 . 2  |-  ( ph  ->  A. x ps )
54dfvd1ir 36943 1  |-  (. ph  ->.  A. x ps ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1442   (.wvd1 36939
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682
This theorem depends on definitions:  df-bi 189  df-vd1 36940
This theorem is referenced by:  tratrbVD  37258  hbimpgVD  37301  hbalgVD  37302  hbexgVD  37303  e2ebindVD  37309
  Copyright terms: Public domain W3C validator