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Theorem nvel 5277
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 5276 . 2 ¬ V ∈ V
2 elex 3465 . 2 (V ∈ 𝐴 → V ∈ V)
31, 2mto 196 1 ¬ V ∈ 𝐴
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wcel 2107  Vcvv 3447
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-sep 5260
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3449
This theorem is referenced by:  curryset  35467  currysetlem3  35470  eliuniincex  43411  eliincex  43412  nvelim  45445
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