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Mirrors > Home > ILE Home > Th. List > elsng | Unicode version |
Description: There is exactly one element in a singleton. Exercise 2 of [TakeutiZaring] p. 15 (generalized). (Contributed by NM, 13-Sep-1995.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
elsng |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2046 | . 2 | |
2 | df-sn 3381 | . 2 | |
3 | 1, 2 | elab2g 2689 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 wcel 1393 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: elsn 3391 elsni 3393 snidg 3400 eltpg 3416 eldifsn 3495 elsucg 4141 funconstss 5285 fniniseg 5287 fniniseg2 5289 ltxr 8695 elfzp12 8961 1exp 9284 |
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