Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  gen12 Structured version   Unicode version

Theorem gen12 28781
Description: Virtual deduction generalizing rule for 2 quantifying variables and 1 virtual hypothesis. gen12 28781 is alrimivv 1643 with virtual deductions. (Contributed by Alan Sare, 2-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
gen12.1  |-  (. ph  ->.  ps
).
Assertion
Ref Expression
gen12  |-  (. ph  ->.  A. x A. y ps
).
Distinct variable groups:    ph, x    ph, y
Allowed substitution hints:    ps( x, y)

Proof of Theorem gen12
StepHypRef Expression
1 gen12.1 . . . 4  |-  (. ph  ->.  ps
).
21in1 28724 . . 3  |-  ( ph  ->  ps )
32alrimivv 1643 . 2  |-  ( ph  ->  A. x A. y ps )
43dfvd1ir 28726 1  |-  (. ph  ->.  A. x A. y ps
).
Colors of variables: wff set class
Syntax hints:   A.wal 1550   (.wvd1 28722
This theorem is referenced by:  sspwtr  28996  pwtrVD  28999  pwtrrVD  29000  suctrALT2VD  29010  truniALTVD  29052  trintALTVD  29054  suctrALTcfVD  29097
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627
This theorem depends on definitions:  df-bi 179  df-vd1 28723
  Copyright terms: Public domain W3C validator