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Theorem neldifsn 4262
Description: The class 𝐴 is not in (𝐵 ∖ {𝐴}). (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
neldifsn ¬ 𝐴 ∈ (𝐵 ∖ {𝐴})

Proof of Theorem neldifsn
StepHypRef Expression
1 neirr 2791 . 2 ¬ 𝐴𝐴
2 eldifsni 4261 . 2 (𝐴 ∈ (𝐵 ∖ {𝐴}) → 𝐴𝐴)
31, 2mto 187 1 ¬ 𝐴 ∈ (𝐵 ∖ {𝐴})
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 1977  wne 2780  cdif 3537  {csn 4125
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ne 2782  df-v 3175  df-dif 3543  df-sn 4126
This theorem is referenced by:  neldifsnd  4263  fofinf1o  8126  dfac9  8841  xrsupss  12011  fvsetsid  15722  islbs3  18976  islindf4  19996  ufinffr  21543  i1fd  23254  nbgranself2  25965  matunitlindflem1  32575  poimirlem25  32604  itg2addnclem  32631  itg2addnclem2  32632  prter2  33184
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