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Theorem disjxsn 4446
 Description: A singleton collection is disjoint. (Contributed by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
disjxsn
Distinct variable group:   ,

Proof of Theorem disjxsn
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfdisj2 4424 . 2
2 moeq 3275 . . 3
3 elsni 4054 . . . . 5
43adantr 465 . . . 4
54moimi 2340 . . 3
62, 5ax-mp 5 . 2
71, 6mpgbir 1622 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  =wceq 1395  e.wcel 1818  E*wmo 2283  {csn 4029  Disj_wdisj 4422 This theorem is referenced by:  disjx0  4447  disjdifprg  27436 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-sn 4030  df-disj 4423
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