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Theorem r19.23v 2599
Description: Theorem 19.23 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 31-Aug-1999.)
Assertion
Ref Expression
r19.23v  |-  ( A. x  e.  A  ( ph  ->  ps )  <->  ( E. x  e.  A  ph  ->  ps ) )
Distinct variable group:    ps, x
Allowed substitution hints:    ph( x)    A( x)

Proof of Theorem r19.23v
StepHypRef Expression
1 nfv 1539 . 2  |-  F/ x ps
21r19.23 2598 1  |-  ( A. x  e.  A  ( ph  ->  ps )  <->  ( E. x  e.  A  ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 105   A.wral 2468   E.wrex 2469
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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-i5r 1546
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-ral 2473  df-rex 2474
This theorem is referenced by:  uniiunlem  3259  dfiin2g  3934  iunss  3942  ralxfr2d  4482  rexxfr2d  4483  ssrel2  4734  reliun  4765  funimaexglem  5318  funimass4  5587  ralrnmpo  6011
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