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Theorem disjx0 4447
 Description: An empty collection is disjoint. (Contributed by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
disjx0

Proof of Theorem disjx0
StepHypRef Expression
1 0ss 3814 . 2
2 disjxsn 4446 . 2
3 disjss1 4428 . 2
41, 2, 3mp2 9 1
 Colors of variables: wff setvar class Syntax hints:  C_wss 3475   c0 3784  {csn 4029  Disj_wdisj 4422 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-rmo 2815  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-sn 4030  df-disj 4423
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