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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2196 |
. 2
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2 | df-sn 3613 |
. 2
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3 | 1, 2 | elab2g 2899 |
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: elsn 3623 elsni 3625 snidg 3636 eltpg 3652 eldifsn 3734 elsucg 4422 funconstss 5655 fniniseg 5657 fniniseg2 5659 fidcenumlemrks 6983 ltxr 9807 elfzp12 10131 1exp 10583 imasaddfnlemg 12794 0subm 12951 0subg 13155 0nsg 13170 kerf1ghm 13230 lsssn0 13703 |
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