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Theorem gen11nv 28694
Description: Virtual deduction generalizing rule for 1 quantifying variable and 1 virtual hypothesis without distinct variables. alrimih 1555 is gen11nv 28694 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 28638 . . 3  |-  ( ph  ->  ps )
41, 3alrimih 1555 . 2  |-  ( ph  ->  A. x ps )
54dfvd1ir 28640 1  |-  (. ph  ->.  A. x ps ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   (.wvd1 28636
This theorem is referenced by:  tratrbVD  28953  hbimpgVD  28996  hbalgVD  28997  hbexgVD  28998  e2ebindVD  29004
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547
This theorem depends on definitions:  df-bi 177  df-vd1 28637
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