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Mirrors > Home > ILE Home > Th. List > snid | Unicode version |
Description: A set is a member of its singleton. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 31-Dec-1993.) |
Ref | Expression |
---|---|
snid.1 |
Ref | Expression |
---|---|
snid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snid.1 | . 2 | |
2 | snidb 3401 | . 2 | |
3 | 1, 2 | mpbi 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1393 cvv 2557 csn 3375 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-sn 3381 |
This theorem is referenced by: vsnid 3403 exsnrex 3413 rabsnt 3445 sneqr 3531 rext 3951 unipw 3953 intid 3960 snnex 4181 ordtriexmidlem2 4246 ordtriexmid 4247 ordtri2orexmid 4248 regexmidlem1 4258 0elsucexmid 4289 ordpwsucexmid 4294 opthprc 4391 fsn 5335 fsn2 5337 fvsn 5358 fvsnun1 5360 acexmidlema 5503 acexmidlemb 5504 acexmidlemab 5506 brtpos0 5867 en1 6279 elreal2 6907 1exp 9284 bj-d0clsepcl 10049 |
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