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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 2663 | . . . 4 | |
2 | 1 | elpw 3486 | . . 3 |
3 | 2 | ralbii 2418 | . 2 |
4 | dfss3 3057 | . 2 | |
5 | unissb 3736 | . 2 | |
6 | 3, 4, 5 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wcel 1465 wral 2393 wss 3041 cpw 3480 cuni 3706 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-v 2662 df-in 3047 df-ss 3054 df-pw 3482 df-uni 3707 |
This theorem is referenced by: pwssb 3868 elpwpw 3869 elpwuni 3872 rintm 3875 dftr4 4001 iotass 5075 tfrlemibfn 6193 tfr1onlembfn 6209 tfrcllembfn 6222 uniixp 6583 fipwssg 6835 unirnioo 9724 restid 12058 topgele 12123 topontopn 12131 unitg 12158 epttop 12186 resttopon 12267 txuni2 12352 txdis 12373 unirnblps 12518 unirnbl 12519 |
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