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Theorem elnotel 9641
Description: A class cannot be an element of one of its elements. (Contributed by AV, 14-Jun-2022.)
Assertion
Ref Expression
elnotel (𝐴𝐵 → ¬ 𝐵𝐴)

Proof of Theorem elnotel
StepHypRef Expression
1 en2lp 9637 . 2 ¬ (𝐴𝐵𝐵𝐴)
21imnani 399 1 (𝐴𝐵 → ¬ 𝐵𝐴)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 2098
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 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-12 2166  ax-ext 2699  ax-sep 5303  ax-nul 5310  ax-pr 5433  ax-reg 9623
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-ne 2938  df-ral 3059  df-rex 3068  df-rab 3431  df-v 3475  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4327  df-if 4533  df-pw 4608  df-sn 4633  df-pr 4635  df-op 4639  df-br 5153  df-opab 5215  df-eprel 5586  df-fr 5637
This theorem is referenced by:  elnel  9642  preleqg  9646  mnurndlem1  43749
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