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Theorem djussxp 4481
 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 3698 . 2
2 snssi 3508 . . 3
3 ssv 2965 . . 3
4 xpss12 4445 . . 3
52, 3, 4sylancl 392 . 2
61, 5mprgbir 2379 1
 Colors of variables: wff set class Syntax hints:   wcel 1393  cvv 2557   wss 2917  csn 3375  ciun 3657   cxp 4343 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-in 2924  df-ss 2931  df-sn 3381  df-iun 3659  df-opab 3819  df-xp 4351 This theorem is referenced by:  djudisj  4750
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