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Theorem vnex 3881
Description: The universal class does not exist. (Contributed by NM, 4-Jul-2005.)
Assertion
Ref Expression
vnex ¬ x x = V

Proof of Theorem vnex
StepHypRef Expression
1 vprc 3879 . 2 ¬ V V
2 isset 2555 . 2 (V V ↔ x x = V)
31, 2mtbi 594 1 ¬ x x = V
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   = wceq 1242  wex 1378   wcel 1390  Vcvv 2551
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-13 1401  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019  ax-sep 3866
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553
This theorem is referenced by: (None)
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