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Mirrors > Home > ILE Home > Th. List > elexd | Unicode version |
Description: If a class is a member of another class, it is a set. (Contributed by Glauco Siliprandi, 11-Oct-2020.) |
Ref | Expression |
---|---|
elexd.1 |
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Ref | Expression |
---|---|
elexd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elexd.1 |
. 2
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2 | elex 2668 |
. 2
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3 | 1, 2 | syl 14 |
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-5 1406 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-v 2659 |
This theorem is referenced by: dmmptd 5211 tfr1onlemsucfn 6191 tfrcllemsucfn 6204 frecrdg 6259 unsnfidcel 6762 fnfi 6777 caseinl 6928 caseinr 6929 acfun 7011 seq3val 10121 seqvalcd 10122 hashennn 10416 lcmval 11587 hashdvds 11739 ennnfonelemp1 11761 isstruct2r 11810 strnfvnd 11819 strfvssn 11821 strslfv2d 11841 setsslid 11849 ressid2 11858 ressval2 11859 istopon 12020 istps 12039 tgclb 12074 restbasg 12177 restco 12183 lmfval 12201 cnfval 12203 cnpfval 12204 cnpval 12206 txcnp 12279 txrest 12284 ismet2 12340 xmetpsmet 12355 mopnval 12428 comet 12485 reldvg 12600 |
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