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Theorem ruv 4228
Description: The Russell class is equal to the universe  _V. Exercise 5 of [TakeutiZaring] p. 22. (Contributed by Alan Sare, 4-Oct-2008.)
Assertion
Ref Expression
ruv  {  |  e/  }  _V

Proof of Theorem ruv
StepHypRef Expression
1 df-v 2553 . 2  _V  {  |  }
2 equid 1586 . . . 4
3 elirrv 4226 . . . . 5
43nelir 2294 . . . 4  e/
52, 42th 163 . . 3  e/
65abbii 2150 . 2  {  |  }  {  |  e/  }
71, 6eqtr2i 2058 1  {  |  e/  }  _V
Colors of variables: wff set class
Syntax hints:   wceq 1242   {cab 2023    e/ wnel 2202   _Vcvv 2551
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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-setind 4220
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ne 2203  df-nel 2204  df-ral 2305  df-v 2553  df-dif 2914  df-sn 3373
This theorem is referenced by:  ruALT  4229
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