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Mirrors > Home > ILE Home > Th. List > elsni | Unicode version |
Description: There is only one element in a singleton. (Contributed by NM, 5-Jun-1994.) |
Ref | Expression |
---|---|
elsni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elsng 3512 | . 2 | |
2 | 1 | ibi 175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 wcel 1465 csn 3497 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-sn 3503 |
This theorem is referenced by: elsn2g 3528 disjsn2 3556 sssnm 3651 disjxsn 3897 pwntru 4092 opth1 4128 elsuci 4295 ordtri2orexmid 4408 onsucsssucexmid 4412 sosng 4582 ressn 5049 funcnvsn 5138 funinsn 5142 fvconst 5576 fmptap 5578 fmptapd 5579 fvunsng 5582 mposnif 5833 1stconst 6086 2ndconst 6087 reldmtpos 6118 tpostpos 6129 1domsn 6681 ac6sfi 6760 onunsnss 6773 snon0 6792 snexxph 6806 elfi2 6828 supsnti 6860 djuf1olem 6906 eldju2ndl 6925 eldju2ndr 6926 difinfsnlem 6952 elreal2 7606 ax1rid 7653 ltxrlt 7798 un0addcl 8978 un0mulcl 8979 elfzonlteqm1 9955 fxnn0nninf 10179 1exp 10290 hashinfuni 10491 hashennnuni 10493 hashprg 10522 zfz1isolemiso 10550 fisumss 11129 sumsnf 11146 fsumsplitsn 11147 fsum2dlemstep 11171 fisumcom2 11175 divalgmod 11551 phi1 11822 dfphi2 11823 exmidunben 11866 txdis1cn 12374 bj-nntrans 13076 bj-nnelirr 13078 pwtrufal 13119 exmidsbthrlem 13144 |
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