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Theorem neldifsnd 4725
 Description: The class 𝐴 is not in (𝐵 ∖ {𝐴}). Deduction form. (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
neldifsnd (𝜑 → ¬ 𝐴 ∈ (𝐵 ∖ {𝐴}))

Proof of Theorem neldifsnd
StepHypRef Expression
1 neldifsn 4724 . 2 ¬ 𝐴 ∈ (𝐵 ∖ {𝐴})
21a1i 11 1 (𝜑 → ¬ 𝐴 ∈ (𝐵 ∖ {𝐴}))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 2107   ∖ cdif 3937  {csn 4564 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2798 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2805  df-cleq 2819  df-clel 2898  df-nfc 2968  df-ne 3022  df-v 3502  df-dif 3943  df-sn 4565 This theorem is referenced by:  difsnb  4738  fsnunf2  6944  rpnnen2lem9  15565  fprodfvdvdsd  15673  ramub1lem1  16352  ramub1lem2  16353  prmdvdsprmo  16368  acsfiindd  17777  gsummgp0  19278  islindf4  20898  gsummatr01lem3  21182  nbgrnself  27055  omsmeas  31467  onint1  33681  bj-fvsnun2  34417  poimirlem30  34789  prtlem80  35864  gneispace0nelrn3  40357  supminfxr2  41610  fsumnncl  41717  fsumsplit1  41718  hoidmv1lelem2  42740  hspmbllem1  42774  hspmbllem2  42775  fsumsplitsndif  43399  mgpsumunsn  44241
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