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Theorem vnex 3890
 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 3888 . 2 ¬ V ∈ V
2 isset 2561 . 2 (V ∈ V ↔ ∃𝑥 𝑥 = V)
31, 2mtbi 595 1 ¬ ∃𝑥 𝑥 = V
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   = wceq 1243  ∃wex 1381   ∈ wcel 1393  Vcvv 2557 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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-13 1404  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022  ax-sep 3875 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559 This theorem is referenced by: (None)
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