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Theorem rexlimiv 2541
Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 20-Nov-1994.)
Hypothesis
Ref Expression
rexlimiv.1  |-  ( x  e.  A  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
rexlimiv  |-  ( E. x  e.  A  ph  ->  ps )
Distinct variable group:    ps, x
Allowed substitution hints:    ph( x)    A( x)

Proof of Theorem rexlimiv
StepHypRef Expression
1 nfv 1508 . 2  |-  F/ x ps
2 rexlimiv.1 . 2  |-  ( x  e.  A  ->  ( ph  ->  ps ) )
31, 2rexlimi 2540 1  |-  ( E. x  e.  A  ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1480   E.wrex 2415
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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-ral 2419  df-rex 2420
This theorem is referenced by:  rexlimiva  2542  rexlimivw  2543  rexlimivv  2553  r19.36av  2580  r19.44av  2588  r19.45av  2589  rexn0  3456  uniss2  3762  elres  4850  ssimaex  5475  tfrlem5  6204  tfrlem8  6208  ecoptocl  6509  mapsn  6577  elixpsn  6622  ixpsnf1o  6623  findcard  6775  findcard2  6776  findcard2s  6777  fiintim  6810  prnmaddl  7291  0re  7759  cnegexlem2  7931  0cnALT  7945  bndndx  8969  uzn0  9334  ublbneg  9398  rexanuz2  10756  opnneiid  12322  bj-inf2vnlem2  13158
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