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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 2177 |
. 2
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2 | elsng 3606 |
. 2
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3 | 1, 2 | mpbiri 168 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-sn 3597 |
This theorem is referenced by: snidb 3621 elsn2g 3624 snnzg 3708 snmg 3709 exmidsssnc 4200 fvunsng 5705 fsnunfv 5712 1stconst 6215 2ndconst 6216 tfr0dm 6316 tfrlemibxssdm 6321 tfrlemi14d 6327 tfr1onlembxssdm 6337 tfr1onlemres 6343 tfrcllembxssdm 6350 tfrcllemres 6356 en1uniel 6797 onunsnss 6909 snon0 6928 supsnti 6997 fseq1p1m1 10067 elfzomin 10179 fsumsplitsnun 11398 divalgmod 11902 setsslid 12482 1strbas 12542 srnginvld 12570 lmodvscad 12584 mgm1 12668 mnd1id 12725 0subm 12748 cnpdis 13375 bj-sels 14288 |
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