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Theorem disjssun 3687
 Description: Subset relation for disjoint classes. (Contributed by NM, 25-Oct-2005.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
disjssun

Proof of Theorem disjssun
StepHypRef Expression
1 indi 3589 . . . . 5
21equncomi 3495 . . . 4
3 uneq2 3497 . . . . 5
4 un0 3654 . . . . 5
53, 4syl6eq 2486 . . . 4
62, 5syl5eq 2482 . . 3
76eqeq1d 2446 . 2
8 df-ss 3336 . 2
9 df-ss 3336 . 2
107, 8, 93bitr4g 281 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wceq 1653   cun 3320   cin 3321   wss 3322  c0 3630 This theorem is referenced by:  hashbclem  11703  alexsubALTlem2  18081  iccntr  18854  reconnlem1  18859  dvne0  19897 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631
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