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Mirrors > Home > ILE Home > Th. List > sspwuni | Unicode version |
Description: Subclass relationship for power class and union. (Contributed by NM, 18-Jul-2006.) |
Ref | Expression |
---|---|
sspwuni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2689 | . . . 4 | |
2 | 1 | elpw 3516 | . . 3 |
3 | 2 | ralbii 2441 | . 2 |
4 | dfss3 3087 | . 2 | |
5 | unissb 3766 | . 2 | |
6 | 3, 4, 5 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wcel 1480 wral 2416 wss 3071 cpw 3510 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-ral 2421 df-v 2688 df-in 3077 df-ss 3084 df-pw 3512 df-uni 3737 |
This theorem is referenced by: pwssb 3898 elpwpw 3899 elpwuni 3902 rintm 3905 dftr4 4031 iotass 5105 tfrlemibfn 6225 tfr1onlembfn 6241 tfrcllembfn 6254 uniixp 6615 fipwssg 6867 unirnioo 9756 restid 12131 topgele 12196 topontopn 12204 unitg 12231 epttop 12259 resttopon 12340 txuni2 12425 txdis 12446 unirnblps 12591 unirnbl 12592 |
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