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Theorem elneq 9636
Description: A class is not equal to any of its elements. (Contributed by AV, 14-Jun-2022.)
Assertion
Ref Expression
elneq (𝐴𝐵𝐴𝐵)

Proof of Theorem elneq
StepHypRef Expression
1 elirr 9635 . 2 ¬ 𝐵𝐵
2 nelelne 3039 . 2 𝐵𝐵 → (𝐴𝐵𝐴𝐵))
31, 2ax-mp 5 1 (𝐴𝐵𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 2106  wne 2938
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-12 2175  ax-ext 2706  ax-sep 5302  ax-pr 5438  ax-reg 9630
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-nf 1781  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ne 2939  df-ral 3060  df-rex 3069  df-v 3480  df-un 3968  df-sn 4632  df-pr 4634
This theorem is referenced by:  nelaneq  9637  preleqg  9653  dfac2b  10169  disjressuc2  38370  oaomoencom  43307  oenassex  43308  tfsconcat0b  43336
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