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Theorem ruv 4474
 Description: The Russell class is equal to the universe . Exercise 5 of [TakeutiZaring] p. 22. (Contributed by Alan Sare, 4-Oct-2008.)
Assertion
Ref Expression
ruv

Proof of Theorem ruv
StepHypRef Expression
1 df-v 2692 . 2
2 equid 1678 . . . 4
3 elirrv 4472 . . . . 5
43nelir 2407 . . . 4
52, 42th 173 . . 3
65abbii 2256 . 2
71, 6eqtr2i 2162 1
 Colors of variables: wff set class Syntax hints:   wceq 1332  cab 2126   wnel 2404  cvv 2690 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-setind 4461 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ne 2310  df-nel 2405  df-ral 2422  df-v 2692  df-dif 3079  df-sn 3539 This theorem is referenced by:  ruALT  4475
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