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Theorem rexxp 4678
 Description: Existential quantification restricted to a cross 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:   ,,,   ,,   ,,   ,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem rexxp
StepHypRef Expression
1 iunxpconst 4594 . . 3
21rexeqi 2629 . 2
3 ralxp.1 . . 3
43rexiunxp 4676 . 2
52, 4bitr3i 185 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1331  wrex 2415  csn 3522  cop 3525  ciun 3808   cxp 4532 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-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-sep 4041  ax-pow 4093  ax-pr 4126 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-rex 2420  df-v 2683  df-sbc 2905  df-csb 2999  df-un 3070  df-in 3072  df-ss 3079  df-pw 3507  df-sn 3528  df-pr 3529  df-op 3531  df-iun 3810  df-opab 3985  df-xp 4540  df-rel 4541 This theorem is referenced by:  rexxpf  4681  fnrnov  5909  foov  5910  ovelimab  5914  xpf1o  6731  cnref1o  9433  txbas  12412
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