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Theorem r19.21v 2554
Description: Theorem 19.21 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 15-Oct-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.)
Assertion
Ref Expression
r19.21v  |-  ( A. x  e.  A  ( ph  ->  ps )  <->  ( ph  ->  A. x  e.  A  ps ) )
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    A( x)

Proof of Theorem r19.21v
StepHypRef Expression
1 nfv 1528 . 2  |-  F/ x ph
21r19.21 2553 1  |-  ( A. x  e.  A  ( ph  ->  ps )  <->  ( ph  ->  A. x  e.  A  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 105   A.wral 2455
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-4 1510  ax-17 1526  ax-ial 1534  ax-i5r 1535
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-ral 2460
This theorem is referenced by:  r19.32vdc  2626  rmo4  2931  rmo3  3055  dftr5  4105  reusv3  4461  tfrlem1  6309  tfrlemi1  6333  tfr1onlemaccex  6349  tfrcllemaccex  6362  tfri3  6368  ordiso2  7034  raluz2  9579  ndvdssub  11935  nninfalllem1  14760  nninfsellemqall  14767
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