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Theorem gen12 31174
Description: Virtual deduction generalizing rule for 2 quantifying variables and 1 virtual hypothesis. gen12 31174 is alrimivv 1691 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 31117 . . 3  |-  ( ph  ->  ps )
32alrimivv 1691 . 2  |-  ( ph  ->  A. x A. y ps )
43dfvd1ir 31119 1  |-  (. ph  ->.  A. x A. y ps
).
Colors of variables: wff setvar class
Syntax hints:   A.wal 1362   (.wvd1 31115
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675
This theorem depends on definitions:  df-bi 185  df-vd1 31116
This theorem is referenced by:  sspwtr  31389  pwtrVD  31394  pwtrrVD  31395  suctrALT2VD  31406  truniALTVD  31448  trintALTVD  31450  suctrALTcfVD  31493
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