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Theorem nvelim 43199
Description: If a class is the universal class it doesn't belong to any class, generalization of nvel 5211. (Contributed by Alexander van der Vekens, 26-May-2017.)
Assertion
Ref Expression
nvelim (𝐴 = V → ¬ 𝐴𝐵)

Proof of Theorem nvelim
StepHypRef Expression
1 nvel 5211 . 2 ¬ V ∈ 𝐵
2 eleq1 2897 . . 3 (V = 𝐴 → (V ∈ 𝐵𝐴𝐵))
32eqcoms 2826 . 2 (𝐴 = V → (V ∈ 𝐵𝐴𝐵))
41, 3mtbii 327 1 (𝐴 = V → ¬ 𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 207   = wceq 1528  wcel 2105  Vcvv 3492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-ext 2790  ax-sep 5194
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-v 3494
This theorem is referenced by:  afvvdm  43217  afvvfunressn  43219  afvvv  43221  afvvfveq  43224
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