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Theorem nev 43342
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 3470 . 2 (𝐴 = V ↔ ∀𝑥 𝑥𝐴)
21necon3abii 2976 1 (𝐴 ≠ V ↔ ¬ ∀𝑥 𝑥𝐴)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 205  wal 1531  wcel 2098  wne 2929  Vcvv 3461
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-ne 2930  df-v 3463
This theorem is referenced by: (None)
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