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Mirrors > Home > ILE Home > Th. List > elun1 | Unicode version |
Description: Membership law for union of classes. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
elun1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssun1 3290 | . 2 | |
2 | 1 | sseli 3143 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2141 cun 3119 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 |
This theorem is referenced by: dcun 3525 exmidundif 4192 exmidundifim 4193 brtposg 6233 dftpos4 6242 dcdifsnid 6483 undifdcss 6900 fidcenumlemrks 6930 djulclr 7026 djulcl 7028 djuss 7047 finomni 7116 hashennnuni 10713 sumsplitdc 11395 srngbased 12541 srngplusgd 12542 srngmulrd 12543 lmodbased 12552 lmodplusgd 12553 lmodscad 12554 ipsbased 12560 ipsaddgd 12561 ipsmulrd 12562 |
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