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Theorem r19.23v 2579
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 1521 . 2  |-  F/ x ps
21r19.23 2578 1  |-  ( A. x  e.  A  ( ph  ->  ps )  <->  ( E. x  e.  A  ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wral 2448   E.wrex 2449
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-17 1519  ax-ial 1527  ax-i5r 1528
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-ral 2453  df-rex 2454
This theorem is referenced by:  uniiunlem  3236  dfiin2g  3906  iunss  3914  ralxfr2d  4449  rexxfr2d  4450  ssrel2  4701  reliun  4732  funimaexglem  5281  funimass4  5547  ralrnmpo  5967
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