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Theorem 2alimi 1679
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 1678 . 2  |-  ( A. y ph  ->  A. y ps )
32alimi 1678 1  |-  ( A. x A. y ph  ->  A. x A. y ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-gen 1663  ax-4 1676
This theorem is referenced by:  2mo  2350  2eu6  2357  euind  3257  reuind  3275  sbnfc2  3826  opelopabt  4732  ssrel  4942  ssrelrel  4954  opabbrex  6347  fnoprabg  6411  tz7.48lem  7169  ssrelf  28223  bj-3exbi  31206  bj-mo3OLD  31417  mpt2bi123f  32370  mptbi12f  32374  ismrc  35512  refimssco  36183  19.33-2  36701  pm11.63  36715  pm11.71  36717  axc5c4c711to11  36726
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