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Theorem neldifsnd 4263
 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 4262 . 2 ¬ 𝐴 ∈ (𝐵 ∖ {𝐴})
21a1i 11 1 (𝜑 → ¬ 𝐴 ∈ (𝐵 ∖ {𝐴}))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 1977   ∖ 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:  difsnb  4278  fsnunf2  6357  rpnnen2lem9  14790  fprodfvdvdsd  14896  ramub1lem1  15568  ramub1lem2  15569  prmdvdsprmo  15584  acsfiindd  17000  gsummgp0  18431  islindf4  19996  gsummatr01lem3  20282  omsmeas  29712  onint1  31618  poimirlem30  32609  prtlem80  33163  gneispace0nelrn3  37460  fsumnncl  38638  fsumsplit1  38639  hoidmv1lelem2  39482  hspmbllem1  39516  hspmbllem2  39517  fsumsplitsndif  40372  nbgrnself  40583  mgpsumunsn  41933
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