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Theorem 2alimi 1570
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 1569 . 2  |-  ( A. y ph  ->  A. y ps )
32alimi 1569 1  |-  ( A. x A. y ph  ->  A. x A. y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1550
This theorem is referenced by:  mo  2304  2mo  2360  2eu6  2367  euind  3122  reuind  3138  sbnfc2  3310  opelopabt  4468  ssrel  4965  ssrelrel  4977  fnoprabg  6172  tz7.48lem  6699  ismrc  26756  19.33-2  27558  pm11.63  27572  pm11.71  27574  ax4567to7  27583  ax7w1AUX7  29646  alcomw9bAUX7  29662
This theorem was proved from axioms:  ax-mp 8  ax-gen 1556  ax-5 1567
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