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Theorem 2alimi 1390
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 1389 . 2  |-  ( A. y ph  ->  A. y ps )
32alimi 1389 1  |-  ( A. x A. y ph  ->  A. x A. y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1287
This theorem was proved from axioms:  ax-mp 7  ax-5 1381  ax-gen 1383
This theorem is referenced by:  mo23  1989  mo3h  2001  spc2gv  2709  spc3gv  2711  euind  2802  reuind  2820  sbnfc2  2988  opelopabt  4089  ssrel  4526  ssrelrel  4538  fnoprabg  5746
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