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Mirrors > Home > ILE Home > Th. List > snidg | Unicode version |
Description: A set is a member of its singleton. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 28-Oct-2003.) |
Ref | Expression |
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snidg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2115 |
. 2
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2 | elsng 3508 |
. 2
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3 | 1, 2 | mpbiri 167 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-sn 3499 |
This theorem is referenced by: snidb 3521 elsn2g 3524 snnzg 3606 snmg 3607 exmidsssnc 4086 fvunsng 5568 fsnunfv 5575 1stconst 6072 2ndconst 6073 tfr0dm 6173 tfrlemibxssdm 6178 tfrlemi14d 6184 tfr1onlembxssdm 6194 tfr1onlemres 6200 tfrcllembxssdm 6207 tfrcllemres 6213 en1uniel 6652 onunsnss 6758 snon0 6776 supsnti 6844 fseq1p1m1 9764 elfzomin 9873 fsumsplitsnun 11077 divalgmod 11469 setsslid 11849 1strbas 11898 srnginvld 11925 lmodvscad 11936 cnpdis 12250 bj-sels 12796 |
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