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Theorem djussxp 5047
 Description: Disjoint union is a subset of a cross product. (Contributed by Stefan O'Rear, 21-Nov-2014.)
Assertion
Ref Expression
djussxp
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem djussxp
StepHypRef Expression
1 iunss 4156 . 2
2 snssi 3966 . . 3
3 ssv 3354 . . 3
4 xpss12 5010 . . 3
52, 3, 4sylancl 645 . 2
61, 5mprgbir 2782 1
 Colors of variables: wff set class Syntax hints:   wcel 1727  cvv 2962   wss 3306  csn 3838  ciun 4117   cxp 4905 This theorem is referenced by:  djudisj  5326  iundom2g  8446 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ral 2716  df-rex 2717  df-v 2964  df-in 3313  df-ss 3320  df-sn 3844  df-iun 4119  df-opab 4292  df-xp 4913
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