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Mirrors > Home > MPE Home > Th. List > vsnid | Structured version Visualization version GIF version |
Description: A setvar variable is a member of its singleton (common case). (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
vsnid | ⊢ 𝑥 ∈ {𝑥} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3203 | . 2 ⊢ 𝑥 ∈ V | |
2 | 1 | snid 4208 | 1 ⊢ 𝑥 ∈ {𝑥} |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1990 {csn 4177 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-sn 4178 |
This theorem is referenced by: exsnrex 4221 rext 4916 unipw 4918 xpdifid 5562 opabiota 6261 fnressn 6425 fressnfv 6427 snnex 6966 snnexOLD 6967 wfrlem14 7428 wfrlem16 7430 findcard2d 8202 ac6sfi 8204 iunfi 8254 elirrv 8504 kmlem2 8973 fin1a2lem10 9231 hsmexlem4 9251 iunfo 9361 fsumsplitsnunOLD 14486 fsumcom2OLD 14506 modfsummodslem1 14524 fprodcom2OLD 14715 lcmfunsnlem2lem1 15351 coprmprod 15375 coprmproddvdslem 15376 lbsextlem4 19161 coe1fzgsumdlem 19671 evl1gsumdlem 19720 frlmlbs 20136 maducoeval2 20446 dishaus 21186 dis2ndc 21263 dislly 21300 dissnlocfin 21332 comppfsc 21335 txdis 21435 txdis1cn 21438 txkgen 21455 isufil2 21712 alexsubALTlem4 21854 tmdgsum 21899 dscopn 22378 ovolfiniun 23269 volfiniun 23315 jensen 24715 uvtxa01vtx0 26297 cplgr1vlem 26325 esum2dlem 30154 bnj1498 31129 cvmlift2lem1 31284 funpartlem 32049 topdifinffinlem 33195 finixpnum 33394 mbfresfi 33456 pclfinN 35186 mzpcompact2lem 37314 fourierdlem48 40371 sge0sup 40608 c0snmgmhm 41914 |
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