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Theorem vprc 4562
 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
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 nalset 4561 . . 3
2 vex 3083 . . . . . . 7
32tbt 345 . . . . . 6
43albii 1685 . . . . 5
5 dfcleq 2415 . . . . 5
64, 5bitr4i 255 . . . 4
76exbii 1712 . . 3
81, 7mtbi 299 . 2
9 isset 3084 . 2
108, 9mtbir 300 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 187  wal 1435   wceq 1437  wex 1657   wcel 1872  cvv 3080 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-8 1874  ax-9 1876  ax-10 1891  ax-12 1909  ax-13 2057  ax-ext 2401  ax-sep 4546 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-v 3082 This theorem is referenced by:  nvel  4563  vnex  4564  intex  4580  intnex  4581  snnex  6611  iprc  6742  elfi2  7937  fi0  7943  ruALT  8125  cardmin2  8440  00lsp  18203  fveqvfvv  38496  ndmaovcl  38575
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