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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 |
---|---|
snidg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2137 | . 2 | |
2 | elsng 3537 | . 2 | |
3 | 1, 2 | mpbiri 167 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 csn 3522 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-sn 3528 |
This theorem is referenced by: snidb 3550 elsn2g 3553 snnzg 3635 snmg 3636 exmidsssnc 4121 fvunsng 5607 fsnunfv 5614 1stconst 6111 2ndconst 6112 tfr0dm 6212 tfrlemibxssdm 6217 tfrlemi14d 6223 tfr1onlembxssdm 6233 tfr1onlemres 6239 tfrcllembxssdm 6246 tfrcllemres 6252 en1uniel 6691 onunsnss 6798 snon0 6817 supsnti 6885 fseq1p1m1 9867 elfzomin 9976 fsumsplitsnun 11181 divalgmod 11613 setsslid 11998 1strbas 12047 srnginvld 12074 lmodvscad 12085 cnpdis 12400 bj-sels 13101 |
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