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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2189 |
. 2
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2 | elsng 3622 |
. 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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-sn 3613 |
This theorem is referenced by: snidb 3637 elsn2g 3640 snnzg 3724 snmg 3725 exmidsssnc 4221 fvunsng 5731 fsnunfv 5738 1stconst 6247 2ndconst 6248 tfr0dm 6348 tfrlemibxssdm 6353 tfrlemi14d 6359 tfr1onlembxssdm 6369 tfr1onlemres 6375 tfrcllembxssdm 6382 tfrcllemres 6388 en1uniel 6831 onunsnss 6946 snon0 6966 supsnti 7035 fseq1p1m1 10126 elfzomin 10238 fsumsplitsnun 11462 divalgmod 11967 setsslid 12566 1strbas 12632 srnginvld 12664 lmodvscad 12682 mgm1 12849 mnd1id 12923 0subm 12951 cnpdis 14219 bj-sels 15144 |
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