Theorem neldifsnd 4796

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

Step	Hyp	Ref	Expression
1		neldifsn 4795	. 2 ⊢ ¬ 𝐴 ∈ (𝐵 ∖ {𝐴})
2	1	a1i 11	1 ⊢ (𝜑 → ¬ 𝐴 ∈ (𝐵 ∖ {𝐴}))

Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 2105   ∖ cdif 3945  {csn 4628

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2702

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-clel 2809  df-ne 2940  df-v 3475  df-dif 3951  df-sn 4629

This theorem is referenced by:  difsnb  4809  fsnunf2  7186  fsumsplit1  15698  rpnnen2lem9  16172  fprodfvdvdsd  16284  ramub1lem1  16966  ramub1lem2  16967  prmdvdsprmo  16982  acsfiindd  18516  gsummgp0  20213  islindf4  21703  gsummatr01lem3  22479  nbgrnself  29050  omsmeas  33787  onint1  35800  bj-fvsnun2  36603  poimirlem30  36984  prtlem80  38197  gneispace0nelrn3  43358  supminfxr2  44640  fsumnncl  44749  hoidmv1lelem2  45769  hspmbllem1  45803  hspmbllem2  45804  fsumsplitsndif  46502  mgpsumunsn  47202