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Theorem vnex 3843
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 3841 . 2 ¬ V V
2 isset 2538 . 2 (V V ↔ x x = V)
31, 2mtbi 582 1 ¬ x x = V
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wex 1362   = wceq 1374   wcel 1376  Vcvv 2534
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 532  ax-in2 533  ax-5 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1378  ax-4 1383  ax-13 1387  ax-14 1388  ax-17 1402  ax-i9 1406  ax-ial 1411  ax-ext 2005  ax-sep 3828
This theorem depends on definitions:  df-bi 110  df-tru 1232  df-fal 1233  df-nf 1330  df-sb 1629  df-clab 2010  df-cleq 2016  df-clel 2019  df-v 2536
This theorem is referenced by: (None)
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