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Theorem nvelim 43847
 Description: If a class is the universal class it doesn't belong to any class, generalization of nvel 5188. (Contributed by Alexander van der Vekens, 26-May-2017.)
Assertion
Ref Expression
nvelim (𝐴 = V → ¬ 𝐴𝐵)

Proof of Theorem nvelim
StepHypRef Expression
1 nvel 5188 . 2 ¬ V ∈ 𝐵
2 eleq1 2877 . . 3 (V = 𝐴 → (V ∈ 𝐵𝐴𝐵))
32eqcoms 2806 . 2 (𝐴 = V → (V ∈ 𝐵𝐴𝐵))
41, 3mtbii 329 1 (𝐴 = V → ¬ 𝐴𝐵)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 209   = wceq 1538   ∈ wcel 2111  Vcvv 3442 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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770  ax-sep 5171 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3444 This theorem is referenced by:  afvvdm  43865  afvvfunressn  43867  afvvv  43869  afvvfveq  43872
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