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Theorem djussxp 4980
 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:   ,
Allowed substitution hint:   ()

Proof of Theorem djussxp
StepHypRef Expression
1 iunss 4206 . 2
2 snssi 4012 . . 3
3 ssv 3371 . . 3
4 xpss12 4940 . . 3
52, 3, 4sylancl 662 . 2
61, 5mprgbir 2781 1
 Colors of variables: wff setvar class Syntax hints:   wcel 1756  cvv 2967   wss 3323  csn 3872  ciun 4166   cxp 4833 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2419 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2715  df-rex 2716  df-v 2969  df-in 3330  df-ss 3337  df-sn 3873  df-iun 4168  df-opab 4346  df-xp 4841 This theorem is referenced by:  djudisj  5260  iundom2g  8696
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