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Theorem 2alimi 1449
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 1448 . 2  |-  ( A. y ph  ->  A. y ps )
32alimi 1448 1  |-  ( A. x A. y ph  ->  A. x A. y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1346
This theorem was proved from axioms:  ax-mp 5  ax-5 1440  ax-gen 1442
This theorem is referenced by:  mo23  2060  mo3h  2072  spc2gv  2821  spc3gv  2823  euind  2917  reuind  2935  sbnfc2  3109  opelopabt  4247  ssrel  4699  ssrelrel  4711  fnoprabg  5954
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