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Theorem r19.21v 2413
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 1437 . 2  |-  F/ x ph
21r19.21 2412 1  |-  ( A. x  e.  A  ( ph  ->  ps )  <->  ( ph  ->  A. x  e.  A  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 102   A.wral 2323
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-4 1416  ax-17 1435  ax-ial 1443  ax-i5r 1444
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-ral 2328
This theorem is referenced by:  r19.32vdc  2476  rmo4  2757  rmo3  2877  dftr5  3885  reusv3  4220  tfrlem1  5954  tfrlemi1  5977  tfri3  5984  rdgon  6004  ordiso2  6415  raluz2  8618  ndvdssub  10242
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