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Theorem gen12 28390
Description: Virtual deduction generalizing rule for 2 quantifying variables and 1 virtual hypothesis. gen12 28390 is alrimivv 1618 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 28339 . . 3  |-  ( ph  ->  ps )
32alrimivv 1618 . 2  |-  ( ph  ->  A. x A. y ps )
43dfvd1ir 28341 1  |-  (. ph  ->.  A. x A. y ps
).
Colors of variables: wff set class
Syntax hints:   A.wal 1527   (.wvd1 28337
This theorem is referenced by:  sspwtr  28595  pwtrVD  28598  pwtrrVD  28600  suctrALT2VD  28612  truniALTVD  28654  trintALTVD  28656  suctrALTcfVD  28699
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603
This theorem depends on definitions:  df-bi 177  df-vd1 28338
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