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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 2146 | . 2 | |
2 | df-sn 3533 | . 2 | |
3 | 1, 2 | elab2g 2831 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1331 wcel 1480 csn 3527 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-sn 3533 |
This theorem is referenced by: elsn 3543 elsni 3545 snidg 3554 eltpg 3569 eldifsn 3650 elsucg 4326 funconstss 5538 fniniseg 5540 fniniseg2 5542 fidcenumlemrks 6841 ltxr 9562 elfzp12 9879 1exp 10322 |
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