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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 {xxx} = V

Proof of Theorem ruv
StepHypRef Expression
1 df-v 2553 . 2 V = {xx = x}
2 equid 1586 . . . 4 x = x
3 elirrv 4226 . . . . 5 ¬ x x
43nelir 2294 . . . 4 xx
52, 42th 163 . . 3 (x = xxx)
65abbii 2150 . 2 {xx = x} = {xxx}
71, 6eqtr2i 2058 1 {xxx} = V
 Colors of variables: wff set class Syntax hints:   = wceq 1242  {cab 2023   ∉ 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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