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Theorem vprc 3888
 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 3887 . . 3
2 vex 2560 . . . . . . 7
32tbt 236 . . . . . 6
43albii 1359 . . . . 5
5 dfcleq 2034 . . . . 5
64, 5bitr4i 176 . . . 4
76exbii 1496 . . 3
81, 7mtbi 595 . 2
9 isset 2561 . 2
108, 9mtbir 596 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 98  wal 1241   wceq 1243  wex 1381   wcel 1393  cvv 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:  nvel  3889  vnex  3890  intexr  3904  intnexr  3905  snnex  4181  ruALT  4275  iprc  4600
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