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Theorem vprc 4055
 Description: The universal class is not a member of itself (and thus is not a set). Proposition 5.21 of [TakeutiZaring] p. 21; our proof, however, does not depend on the Axiom of Regularity. (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
vprc

Proof of Theorem vprc
StepHypRef Expression
1 vnex 4054 . 2
2 isset 2687 . 2
31, 2mtbir 660 1
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1331  wex 1468   wcel 1480  cvv 2681 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 2119  ax-sep 4041 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-v 2683 This theorem is referenced by:  nvel  4056  intexr  4070  intnexr  4071  abnex  4363  snnex  4364  ruALT  4461  dcextest  4490  iprc  4802  snexxph  6831  elfi2  6853  fi0  6856
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