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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 2203 | . . . . 5 | |
2 | eleq1 2202 | . . . . 5 | |
3 | 1, 2 | anbi12d 464 | . . . 4 |
4 | 3 | spcegv 2774 | . . 3 |
5 | 4 | anabsi7 570 | . 2 |
6 | eluni 3739 | . 2 | |
7 | 5, 6 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wex 1468 wcel 1480 cuni 3736 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-uni 3737 |
This theorem is referenced by: ssuni 3758 unipw 4139 opeluu 4371 sucunielr 4426 unon 4427 ordunisuc2r 4430 tfrlemibxssdm 6224 tfr1onlemsucaccv 6238 tfr1onlembxssdm 6240 tfrcllemsucaccv 6251 tfrcllembxssdm 6253 tgss2 12248 neipsm 12323 unirnblps 12591 unirnbl 12592 blbas 12602 |
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