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Theorem 2alimi 1547
Description: Inference doubly quantifying both antecedent and consequent. (Contributed by NM, 3-Feb-2005.)
Hypothesis
Ref Expression
alimi.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
2alimi  |-  ( A. x A. y ph  ->  A. x A. y ps )

Proof of Theorem 2alimi
StepHypRef Expression
1 alimi.1 . . 3  |-  ( ph  ->  ps )
21alimi 1546 . 2  |-  ( A. y ph  ->  A. y ps )
32alimi 1546 1  |-  ( A. x A. y ph  ->  A. x A. y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527
This theorem is referenced by:  mo  2165  2mo  2221  2eu6  2228  euind  2952  reuind  2968  sbnfc2  3141  opelopabt  4277  ssrel  4776  ssrelrel  4787  fnoprabg  5945  tz7.48lem  6453  ismrc  26776  19.33-2  27580  pm11.63  27594  pm11.71  27596  ax4567to7  27605  hbae-x12  29109
This theorem was proved from axioms:  ax-mp 8  ax-gen 1533  ax-5 1544
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