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Theorem gen22 28394
Description: Virtual deduction generalizing rule for 2 quantifying variables and 2 virtual hypothesis. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
gen22.1  |-  (. ph ,. ps  ->.  ch ).
Assertion
Ref Expression
gen22  |-  (. ph ,. ps  ->.  A. x A. y ch ).
Distinct variable groups:    ph, x    ph, y    ps, x    ps, y
Allowed substitution hints:    ch( x, y)

Proof of Theorem gen22
StepHypRef Expression
1 gen22.1 . . . . 5  |-  (. ph ,. ps  ->.  ch ).
21dfvd2i 28354 . . . 4  |-  ( ph  ->  ( ps  ->  ch ) )
32alrimdv 1619 . . 3  |-  ( ph  ->  ( ps  ->  A. y ch ) )
43alrimdv 1619 . 2  |-  ( ph  ->  ( ps  ->  A. x A. y ch ) )
54dfvd2ir 28355 1  |-  (. ph ,. ps  ->.  A. x A. y ch ).
Colors of variables: wff set class
Syntax hints:   A.wal 1527   (.wvd2 28346
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-an 360  df-vd2 28347
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