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Theorem sndisj 4444
 Description: Any collection of singletons is disjoint. (Contributed by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
sndisj

Proof of Theorem sndisj
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfdisj2 4424 . 2
2 moeq 3275 . . 3
3 simpr 461 . . . . . 6
4 elsn 4043 . . . . . 6
53, 4sylib 196 . . . . 5
65eqcomd 2465 . . . 4
76moimi 2340 . . 3
82, 7ax-mp 5 . 2
91, 8mpgbir 1622 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  e.wcel 1818  E*wmo 2283  {csn 4029  Disj_wdisj 4422 This theorem is referenced by:  0disj  4445  sibfof  28282 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-rmo 2815  df-v 3111  df-sn 4030  df-disj 4423
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