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Theorem djudisj 5439
Description: Disjoint unions with disjoint index sets are disjoint. (Contributed by Stefan O'Rear, 21-Nov-2014.)
Assertion
Ref Expression
djudisj
Distinct variable groups:   ,   ,

Proof of Theorem djudisj
StepHypRef Expression
1 djussxp 5153 . 2
2 incom 3690 . . 3
3 djussxp 5153 . . . 4
4 incom 3690 . . . . 5
5 xpdisj1 5433 . . . . 5
64, 5syl5eq 2510 . . . 4
7 ssdisj 3876 . . . 4
83, 6, 7sylancr 663 . . 3
92, 8syl5eq 2510 . 2
10 ssdisj 3876 . 2
111, 9, 10sylancr 663 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395   cvv 3109  i^icin 3474  C_wss 3475   c0 3784  {csn 4029  U_ciun 4330  X.cxp 5002
This theorem is referenced by:  ackbij1lem9  8629
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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
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-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-iun 4332  df-opab 4511  df-xp 5010  df-rel 5011
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