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Theorem nvel 4991
Description: The universal class does not belong to any class. (Contributed by FL, 31-Dec-2006.)
Assertion
Ref Expression
nvel ¬ V ∈ 𝐴

Proof of Theorem nvel
StepHypRef Expression
1 vprc 4990 . 2 ¬ V ∈ V
2 elex 3398 . 2 (V ∈ 𝐴 → V ∈ V)
31, 2mto 189 1 ¬ V ∈ 𝐴
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 2157  Vcvv 3383
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-8 2159  ax-9 2166  ax-12 2213  ax-13 2354  ax-ext 2775  ax-sep 4973
This theorem depends on definitions:  df-bi 199  df-an 386  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2784  df-cleq 2790  df-clel 2793  df-v 3385
This theorem is referenced by:  eliuniincex  40038  eliincex  40039  nvelim  41965
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