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Theorem 2alimi 1550
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 1549 . 2  |-  ( A. y ph  ->  A. y ps )
32alimi 1549 1  |-  ( A. x A. y ph  ->  A. x A. y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530
This theorem is referenced by:  mo  2178  2mo  2234  2eu6  2241  euind  2965  reuind  2981  sbnfc2  3154  opelopabt  4293  ssrel  4792  ssrelrel  4803  fnoprabg  5961  tz7.48lem  6469  ismrc  26879  19.33-2  27683  pm11.63  27697  pm11.71  27699  ax4567to7  27708  alcomw9bAUX7  29631  hbae-x12  29731
This theorem was proved from axioms:  ax-mp 8  ax-gen 1536  ax-5 1547
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