Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  nev Structured version   Visualization version   GIF version

Theorem nev 40327
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 3488 . 2 (𝐴 = V ↔ ∀𝑥 𝑥𝐴)
21necon3abii 3060 1 (𝐴 ≠ V ↔ ¬ ∀𝑥 𝑥𝐴)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 209  wal 1536  wcel 2115  wne 3014  Vcvv 3480
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-ne 3015  df-v 3482
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator