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Theorem 2alimi 1432
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 1431 . 2  |-  ( A. y ph  ->  A. y ps )
32alimi 1431 1  |-  ( A. x A. y ph  ->  A. x A. y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1329
This theorem was proved from axioms:  ax-mp 5  ax-5 1423  ax-gen 1425
This theorem is referenced by:  mo23  2038  mo3h  2050  spc2gv  2771  spc3gv  2773  euind  2866  reuind  2884  sbnfc2  3055  opelopabt  4179  ssrel  4622  ssrelrel  4634  fnoprabg  5865
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