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Theorem nvelim 45508
Description: If a class is the universal class it doesn't belong to any class, generalization of nvel 5293. (Contributed by Alexander van der Vekens, 26-May-2017.)
Assertion
Ref Expression
nvelim (𝐴 = V → ¬ 𝐴𝐵)

Proof of Theorem nvelim
StepHypRef Expression
1 nvel 5293 . 2 ¬ V ∈ 𝐵
2 eleq1 2820 . . 3 (V = 𝐴 → (V ∈ 𝐵𝐴𝐵))
32eqcoms 2739 . 2 (𝐴 = V → (V ∈ 𝐵𝐴𝐵))
41, 3mtbii 325 1 (𝐴 = V → ¬ 𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 205   = wceq 1541  wcel 2106  Vcvv 3459
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2702  ax-sep 5276
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2709  df-cleq 2723  df-clel 2809  df-v 3461
This theorem is referenced by:  afvvdm  45526  afvvfunressn  45528  afvvv  45530  afvvfveq  45533
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