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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 2147 |
. 2
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2 | df-sn 3538 |
. 2
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3 | 1, 2 | elab2g 2835 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-sn 3538 |
This theorem is referenced by: elsn 3548 elsni 3550 snidg 3561 eltpg 3576 eldifsn 3658 elsucg 4334 funconstss 5546 fniniseg 5548 fniniseg2 5550 fidcenumlemrks 6849 ltxr 9592 elfzp12 9910 1exp 10353 |
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