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Mirrors > Home > ILE Home > Th. List > elpw2g | Unicode version |
Description: Membership in a power class. Theorem 86 of [Suppes] p. 47. (Contributed by NM, 7-Aug-2000.) |
Ref | Expression |
---|---|
elpw2g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elpwi 3489 | . 2 | |
2 | ssexg 4037 | . . . 4 | |
3 | elpwg 3488 | . . . . 5 | |
4 | 3 | biimparc 297 | . . . 4 |
5 | 2, 4 | syldan 280 | . . 3 |
6 | 5 | expcom 115 | . 2 |
7 | 1, 6 | impbid2 142 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wcel 1465 cvv 2660 wss 3041 cpw 3480 |
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 ax-sep 4016 |
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-v 2662 df-in 3047 df-ss 3054 df-pw 3482 |
This theorem is referenced by: elpw2 4052 pwnss 4053 elfir 6829 istopg 12093 uniopn 12095 iscld 12199 ntrval 12206 clsval 12207 discld 12232 neival 12239 isnei 12240 restdis 12280 cnpfval 12291 cndis 12337 blfvalps 12481 blfps 12505 blf 12506 reldvg 12744 |
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