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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 |
---|---|
snid.1 |
Ref | Expression |
---|---|
snid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snid.1 | . 2 | |
2 | snidb 3555 | . 2 | |
3 | 1, 2 | mpbi 144 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 cvv 2686 csn 3527 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-sn 3533 |
This theorem is referenced by: vsnid 3557 exsnrex 3566 rabsnt 3598 sneqr 3687 undifexmid 4117 exmidexmid 4120 exmid01 4121 exmidundif 4129 exmidundifim 4130 unipw 4139 intid 4146 ordtriexmidlem2 4436 ordtriexmid 4437 ordtri2orexmid 4438 regexmidlem1 4448 0elsucexmid 4480 ordpwsucexmid 4485 opthprc 4590 fsn 5592 fsn2 5594 fvsn 5615 fvsnun1 5617 acexmidlema 5765 acexmidlemb 5766 acexmidlemab 5768 brtpos0 6149 mapsn 6584 mapsncnv 6589 0elixp 6623 en1 6693 djulclr 6934 djurclr 6935 djulcl 6936 djurcl 6937 djuf1olem 6938 exmidonfinlem 7049 elreal2 7638 1exp 10322 hashinfuni 10523 ennnfonelemhom 11928 dvef 12856 djucllem 13007 bj-d0clsepcl 13123 exmid1stab 13195 |
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