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Theorem djussxp 5153
Description: Disjoint union is a subset of a Cartesian product. (Contributed by Stefan O'Rear, 21-Nov-2014.)
Assertion
Ref Expression
djussxp
Distinct variable group:   ,

Proof of Theorem djussxp
StepHypRef Expression
1 iunss 4371 . 2
2 snssi 4174 . . 3
3 ssv 3523 . . 3
4 xpss12 5113 . . 3
52, 3, 4sylancl 662 . 2
61, 5mprgbir 2821 1
Colors of variables: wff setvar class
Syntax hints:  e.wcel 1818   cvv 3109  C_wss 3475  {csn 4029  U_ciun 4330  X.cxp 5002
This theorem is referenced by:  djudisj  5439  iundom2g  8936
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
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-ral 2812  df-rex 2813  df-v 3111  df-in 3482  df-ss 3489  df-sn 4030  df-iun 4332  df-opab 4511  df-xp 5010
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