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Theorem rexxp 5150
 Description: Existential quantification restricted to a Cartesian product is equivalent to a double restricted quantification. (Contributed by NM, 11-Nov-1995.) (Revised by Mario Carneiro, 14-Feb-2015.)
Hypothesis
Ref Expression
ralxp.1
Assertion
Ref Expression
rexxp
Distinct variable groups:   ,,,   ,,   ,,   ,   ,

Proof of Theorem rexxp
StepHypRef Expression
1 iunxpconst 5061 . . 3
21rexeqi 3059 . 2
3 ralxp.1 . . 3
43rexiunxp 5148 . 2
52, 4bitr3i 251 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  E.wrex 2808  {csn 4029  <.cop 4035  U_ciun 4330  X.cxp 5002 This theorem is referenced by:  exopxfr  5151  fnrnov  6448  foov  6449  ovelimab  6453  el2xptp  6843  xpf1o  7699  xpwdomg  8032  hsmexlem2  8828  cnref1o  11244  vdwmc  14496  arwhoma  15372  txbas  20068  txkgen  20153  xrofsup  27582  elunirnmbfm  28224  rmxypairf1o  30847  unxpwdom3  31041 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-iun 4332  df-opab 4511  df-xp 5010  df-rel 5011
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