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Theorem bj-vprc 9459
Description: vprc 3882 from bounded separation. (Contributed by BJ, 18-Nov-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-vprc ¬ V V

Proof of Theorem bj-vprc
Dummy variables x y are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bj-nalset 9458 . . 3 ¬ xy y x
2 vex 2557 . . . . . . 7 y V
32tbt 236 . . . . . 6 (y x ↔ (y xy V))
43albii 1359 . . . . 5 (y y xy(y xy V))
5 dfcleq 2034 . . . . 5 (x = V ↔ y(y xy V))
64, 5bitr4i 176 . . . 4 (y y xx = V)
76exbii 1496 . . 3 (xy y xx x = V)
81, 7mtbi 595 . 2 ¬ x x = V
9 isset 2558 . 2 (V V ↔ x x = V)
108, 9mtbir 596 1 ¬ V V
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 98  wal 1241   = wceq 1243  wex 1381   wcel 1393  Vcvv 2554
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-bdn 9380  ax-bdel 9384  ax-bdsep 9447
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 2556
This theorem is referenced by:  bj-nvel  9460  bj-vnex  9461  bj-intexr  9471  bj-intnexr  9472
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