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Theorem elndif 3696
 Description: A set does not belong to a class excluding it. (Contributed by NM, 27-Jun-1994.)
Assertion
Ref Expression
elndif (𝐴𝐵 → ¬ 𝐴 ∈ (𝐶𝐵))

Proof of Theorem elndif
StepHypRef Expression
1 eldifn 3695 . 2 (𝐴 ∈ (𝐶𝐵) → ¬ 𝐴𝐵)
21con2i 133 1 (𝐴𝐵 → ¬ 𝐴 ∈ (𝐶𝐵))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 1977   ∖ cdif 3537 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-v 3175  df-dif 3543 This theorem is referenced by:  peano5  6981  extmptsuppeq  7206  undifixp  7830  ssfin4  9015  isf32lem3  9060  isf34lem4  9082  xrinfmss  12012  restntr  20796  cmpcld  21015  reconnlem2  22438  lebnumlem1  22568  i1fd  23254  dfon2lem6  30937  onsucconi  31606  meaiininclem  39376  caragendifcl  39404
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