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Theorem 2alimi 1467
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 1466 . 2  |-  ( A. y ph  ->  A. y ps )
32alimi 1466 1  |-  ( A. x A. y ph  ->  A. x A. y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1362
This theorem was proved from axioms:  ax-mp 5  ax-5 1458  ax-gen 1460
This theorem is referenced by:  mo23  2083  mo3h  2095  spc2gv  2851  spc3gv  2853  euind  2947  reuind  2965  sbnfc2  3141  opelopabt  4291  ssrel  4743  ssrelrel  4755  fnoprabg  6011
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