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Theorem ruv 4208
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 2533 . 2 V = {xx = x}
2 equid 1567 . . . 4 x = x
3 elirrv 4206 . . . . 5 ¬ x x
43nelir 2274 . . . 4 xx
52, 42th 163 . . 3 (x = xxx)
65abbii 2131 . 2 {xx = x} = {xxx}
71, 6eqtr2i 2039 1 {xxx} = V
Colors of variables: wff set class
Syntax hints:   = wceq 1226  {cab 2004  wnel 2183  Vcvv 2531
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 532  ax-in2 533  ax-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000  ax-setind 4200
This theorem depends on definitions:  df-bi 110  df-3an 873  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-ne 2184  df-nel 2185  df-ral 2285  df-v 2533  df-dif 2893  df-sn 3352
This theorem is referenced by:  ruALT  4209
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