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Mirrors > Home > ILE Home > Th. List > elunii | Unicode version |
Description: Membership in class union. (Contributed by NM, 24-Mar-1995.) |
Ref | Expression |
---|---|
elunii |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq2 2234 | . . . . 5 | |
2 | eleq1 2233 | . . . . 5 | |
3 | 1, 2 | anbi12d 470 | . . . 4 |
4 | 3 | spcegv 2818 | . . 3 |
5 | 4 | anabsi7 576 | . 2 |
6 | eluni 3797 | . 2 | |
7 | 5, 6 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wex 1485 wcel 2141 cuni 3794 |
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-uni 3795 |
This theorem is referenced by: ssuni 3816 unipw 4200 opeluu 4433 sucunielr 4492 unon 4493 ordunisuc2r 4496 tfrlemibxssdm 6303 tfr1onlemsucaccv 6317 tfr1onlembxssdm 6319 tfrcllemsucaccv 6330 tfrcllembxssdm 6332 tgss2 12832 neipsm 12907 unirnblps 13175 unirnbl 13176 blbas 13186 |
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