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Theorem 0disj 4419
 Description: Any collection of empty sets is disjoint. (Contributed by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
0disj Disj

Proof of Theorem 0disj
StepHypRef Expression
1 0ss 3797 . . 3
21rgenw 2793 . 2
3 sndisj 4418 . 2 Disj
4 disjss2 4400 . 2 Disj Disj
52, 3, 4mp2 9 1 Disj
 Colors of variables: wff setvar class Syntax hints:  wral 2782   wss 3442  c0 3767  csn 4002  Disj wdisj 4397 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-eu 2270  df-mo 2271  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ral 2787  df-rmo 2790  df-v 3089  df-dif 3445  df-in 3449  df-ss 3456  df-nul 3768  df-sn 4003  df-disj 4398 This theorem is referenced by: (None)
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