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Theorem nev 39011
Description: Express that not every set is in a class. (Contributed by RP, 16-Apr-2020.)
Assertion
Ref Expression
nev (𝐴 ≠ V ↔ ¬ ∀𝑥 𝑥𝐴)
Distinct variable group:   𝑥,𝐴

Proof of Theorem nev
StepHypRef Expression
1 eqv 3404 . 2 (𝐴 = V ↔ ∀𝑥 𝑥𝐴)
21necon3abii 3014 1 (𝐴 ≠ V ↔ ¬ ∀𝑥 𝑥𝐴)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 198  wal 1599  wcel 2106  wne 2968  Vcvv 3397
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2054  ax-9 2115  ax-12 2162  ax-ext 2753
This theorem depends on definitions:  df-bi 199  df-an 387  df-tru 1605  df-ex 1824  df-sb 2012  df-clab 2763  df-cleq 2769  df-clel 2773  df-ne 2969  df-v 3399
This theorem is referenced by: (None)
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