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Mirrors > Home > ILE Home > Th. List > snid | Unicode version |
Description: A set is a member of its singleton. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 31-Dec-1993.) |
Ref | Expression |
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snid.1 |
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Ref | Expression |
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snid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snid.1 |
. 2
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2 | snidb 3519 |
. 2
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3 | 1, 2 | mpbi 144 |
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 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 |
This theorem depends on definitions: df-bi 116 df-tru 1315 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-v 2657 df-sn 3497 |
This theorem is referenced by: vsnid 3521 exsnrex 3530 rabsnt 3562 sneqr 3651 undifexmid 4075 exmidexmid 4078 exmid01 4079 exmidundif 4087 exmidundifim 4088 unipw 4097 intid 4104 ordtriexmidlem2 4394 ordtriexmid 4395 ordtri2orexmid 4396 regexmidlem1 4406 0elsucexmid 4438 ordpwsucexmid 4443 opthprc 4548 fsn 5544 fsn2 5546 fvsn 5567 fvsnun1 5569 acexmidlema 5717 acexmidlemb 5718 acexmidlemab 5720 brtpos0 6101 mapsn 6536 mapsncnv 6541 0elixp 6575 en1 6645 djulclr 6884 djurclr 6885 djulcl 6886 djurcl 6887 djuf1olem 6888 elreal2 7559 1exp 10209 hashinfuni 10410 ennnfonelemhom 11767 djucllem 12690 bj-d0clsepcl 12806 |
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