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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 |
Ref | Expression |
---|---|
elexd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elexd.1 | . 2 | |
2 | elex 2732 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2135 cvv 2721 |
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-5 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-v 2723 |
This theorem is referenced by: ifexd 4456 dmmptd 5312 tfr1onlemsucfn 6299 tfrcllemsucfn 6312 frecrdg 6367 unsnfidcel 6877 fnfi 6893 caseinl 7047 caseinr 7048 omniwomnimkv 7122 acfun 7154 seq3val 10383 seqvalcd 10384 hashennn 10682 lcmval 11974 hashdvds 12132 ennnfonelemp1 12282 isstruct2r 12348 strnfvnd 12357 strfvssn 12359 strslfv2d 12379 setsslid 12387 ressid2 12396 ressval2 12397 istopon 12558 istps 12577 tgclb 12612 restbasg 12715 restco 12721 lmfval 12739 cnfval 12741 cnpfval 12742 cnpval 12745 txcnp 12818 txrest 12823 ismet2 12901 xmetpsmet 12916 mopnval 12989 comet 13046 reldvg 13195 dvmptclx 13227 |
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