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Theorem vnex 4059
 Description: The universal class does not exist as a set. (Contributed by NM, 4-Jul-2005.)
Assertion
Ref Expression
vnex

Proof of Theorem vnex
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nalset 4058 . 2
2 vex 2689 . . . . . 6
32tbt 246 . . . . 5
43albii 1446 . . . 4
5 dfcleq 2133 . . . 4
64, 5bitr4i 186 . . 3
76exbii 1584 . 2
81, 7mtbi 659 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 104  wal 1329   wceq 1331  wex 1468   wcel 1480  cvv 2686 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-13 1491  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2121  ax-sep 4046 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-v 2688 This theorem is referenced by:  vprc  4060
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