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Theorem nvel 4720
Description: The universal class doesn't belong to any class. (Contributed by FL, 31-Dec-2006.)
Assertion
Ref Expression
nvel ¬ V ∈ 𝐴

Proof of Theorem nvel
StepHypRef Expression
1 vprc 4719 . 2 ¬ V ∈ V
2 elex 3184 . 2 (V ∈ 𝐴 → V ∈ V)
31, 2mto 186 1 ¬ V ∈ 𝐴
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 1976  Vcvv 3172
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-8 1978  ax-9 1985  ax-12 2033  ax-13 2233  ax-ext 2589  ax-sep 4703
This theorem depends on definitions:  df-bi 195  df-an 384  df-tru 1477  df-ex 1695  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-v 3174
This theorem is referenced by:  eliuniincex  38119  eliincex  38120  nvelim  39646
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