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Mirrors > Home > ILE Home > Th. List > velsn | Unicode version |
Description: There is only one element in a singleton. Exercise 2 of [TakeutiZaring] p. 15. (Contributed by NM, 21-Jun-1993.) |
Ref | Expression |
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velsn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2660 |
. 2
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2 | 1 | elsn 3509 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-sn 3499 |
This theorem is referenced by: dfpr2 3512 mosn 3526 ralsnsg 3527 ralsns 3528 rexsns 3529 disjsn 3551 snprc 3554 euabsn2 3558 prmg 3610 snss 3615 difprsnss 3624 eqsnm 3648 snsssn 3654 snsspw 3657 dfnfc2 3720 uni0b 3727 uni0c 3728 sndisj 3891 unidif0 4051 exmid01 4081 rext 4097 exss 4109 frirrg 4232 ordsucim 4376 ordtriexmidlem 4395 ordtri2or2exmidlem 4401 onsucelsucexmidlem 4404 elirr 4416 sucprcreg 4424 fconstmpt 4546 opeliunxp 4554 dmsnopg 4968 dfmpt3 5203 nfunsn 5409 fsn 5546 fnasrn 5552 fnasrng 5554 fconstfvm 5592 eusvobj2 5714 opabex3d 5973 opabex3 5974 dcdifsnid 6354 ecexr 6388 ixp0x 6574 xpsnen 6668 fidifsnen 6717 difinfsn 6937 iccid 9601 fzsn 9739 fzpr 9750 fzdifsuc 9754 fsum2dlemstep 11095 ef0lem 11217 1nprm 11641 restsn 12192 |
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