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Theorem elnotel 9057
 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 9053 . 2 ¬ (𝐴𝐵𝐵𝐴)
21imnani 404 1 (𝐴𝐵 → ¬ 𝐵𝐴)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 2115 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5184  ax-nul 5191  ax-pr 5311  ax-reg 9040 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-mo 2624  df-eu 2655  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ne 3014  df-ral 3137  df-rex 3138  df-rab 3141  df-v 3481  df-sbc 3758  df-dif 3921  df-un 3923  df-in 3925  df-ss 3935  df-nul 4275  df-if 4449  df-sn 4549  df-pr 4551  df-op 4555  df-br 5048  df-opab 5110  df-eprel 5446  df-fr 5495 This theorem is referenced by:  elnel  9058  preleqg  9062  mnurndlem1  40825
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