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Theorem gen11nv 31636
Description: Virtual deduction generalizing rule for 1 quantifying variable and 1 virtual hypothesis without distinct variables. alrimih 1613 is gen11nv 31636 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 31581 . . 3  |-  ( ph  ->  ps )
41, 3alrimih 1613 . 2  |-  ( ph  ->  A. x ps )
54dfvd1ir 31583 1  |-  (. ph  ->.  A. x ps ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1368   (.wvd1 31579
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603
This theorem depends on definitions:  df-bi 185  df-vd1 31580
This theorem is referenced by:  tratrbVD  31894  hbimpgVD  31937  hbalgVD  31938  hbexgVD  31939  e2ebindVD  31945
  Copyright terms: Public domain W3C validator