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Theorem neldifsn 4354
 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 2832 . 2 ¬ 𝐴𝐴
2 eldifsni 4353 . 2 (𝐴 ∈ (𝐵 ∖ {𝐴}) → 𝐴𝐴)
31, 2mto 188 1 ¬ 𝐴 ∈ (𝐵 ∖ {𝐴})
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ∈ wcel 2030   ≠ wne 2823   ∖ cdif 3604  {csn 4210 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ne 2824  df-v 3233  df-dif 3610  df-sn 4211 This theorem is referenced by:  neldifsnd  4355  fofinf1o  8282  dfac9  8996  xrsupss  12177  fvsetsid  15937  islbs3  19203  islindf4  20225  ufinffr  21780  i1fd  23493  finsumvtxdg2sstep  26501  matunitlindflem1  33535  poimirlem25  33564  itg2addnclem  33591  itg2addnclem2  33592  prter2  34485
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