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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 3550 | . 2 | |
3 | 1, 2 | mpbi 144 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 cvv 2681 csn 3522 |
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 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-sn 3528 |
This theorem is referenced by: vsnid 3552 exsnrex 3561 rabsnt 3593 sneqr 3682 undifexmid 4112 exmidexmid 4115 exmid01 4116 exmidundif 4124 exmidundifim 4125 unipw 4134 intid 4141 ordtriexmidlem2 4431 ordtriexmid 4432 ordtri2orexmid 4433 regexmidlem1 4443 0elsucexmid 4475 ordpwsucexmid 4480 opthprc 4585 fsn 5585 fsn2 5587 fvsn 5608 fvsnun1 5610 acexmidlema 5758 acexmidlemb 5759 acexmidlemab 5761 brtpos0 6142 mapsn 6577 mapsncnv 6582 0elixp 6616 en1 6686 djulclr 6927 djurclr 6928 djulcl 6929 djurcl 6930 djuf1olem 6931 exmidonfinlem 7042 elreal2 7631 1exp 10315 hashinfuni 10516 ennnfonelemhom 11917 dvef 12845 djucllem 12996 bj-d0clsepcl 13112 exmid1stab 13184 |
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