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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 2177 | . 2 | |
2 | df-sn 3587 | . 2 | |
3 | 1, 2 | elab2g 2877 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1348 wcel 2141 csn 3581 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-sn 3587 |
This theorem is referenced by: elsn 3597 elsni 3599 snidg 3610 eltpg 3626 eldifsn 3708 elsucg 4387 funconstss 5612 fniniseg 5614 fniniseg2 5616 fidcenumlemrks 6927 ltxr 9721 elfzp12 10044 1exp 10494 0subm 12691 |
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