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Theorem snexprc 4119
 Description: A singleton whose element is a proper class is a set. The case of Theorem 7.12 of [Quine] p. 51, proved using only Extensionality, Power Set, and Separation. Replacement is not needed. (Contributed by Jim Kingdon, 1-Sep-2018.)
Assertion
Ref Expression
snexprc

Proof of Theorem snexprc
StepHypRef Expression
1 snprc 3597 . . 3
21biimpi 119 . 2
3 0ex 4064 . 2
42, 3eqeltrdi 2231 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1332   wcel 1481  cvv 2690  c0 3369  csn 3533 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-nul 4063 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-fal 1338  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-dif 3079  df-nul 3370  df-sn 3539 This theorem is referenced by:  notnotsnex  4120
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