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Mirrors > Home > ILE Home > Th. List > snexprc | Unicode version |
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.) |
Ref | Expression |
---|---|
snexprc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snprc 3635 | . . 3 | |
2 | 1 | biimpi 119 | . 2 |
3 | 0ex 4103 | . 2 | |
4 | 2, 3 | eqeltrdi 2255 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1342 wcel 2135 cvv 2721 c0 3404 csn 3570 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 ax-nul 4102 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-dif 3113 df-nul 3405 df-sn 3576 |
This theorem is referenced by: notnotsnex 4160 |
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