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Theorem disjors 4438
Description: Two ways to say that a collection ( ) for is disjoint. (Contributed by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
disjors
Distinct variable groups:   , , ,   , ,

Proof of Theorem disjors
StepHypRef Expression
1 nfcv 2619 . . 3
2 nfcsb1v 3450 . . 3
3 csbeq1a 3443 . . 3
41, 2, 3cbvdisj 4432 . 2
5 csbeq1 3437 . . 3
65disjor 4436 . 2
74, 6bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  \/wo 368  =wceq 1395  A.wral 2807  [_csb 3434  i^icin 3474   c0 3784  Disj_wdisj 4422
This theorem is referenced by:  disji2  4439  disjprg  4448  disjxiun  4449  disjxun  4450  iundisj2  21959  disji2f  27438  disjpreima  27445  disjxpin  27447  iundisj2f  27449  disjunsn  27453  iundisj2fi  27602
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-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-reu 2814  df-rmo 2815  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-in 3482  df-nul 3785  df-disj 4423
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