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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 3514 | . 2 | |
2 | ssexg 4062 | . . . 4 | |
3 | elpwg 3513 | . . . . 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 1480 cvv 2681 wss 3066 cpw 3505 |
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 2119 ax-sep 4041 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-in 3072 df-ss 3079 df-pw 3507 |
This theorem is referenced by: elpw2 4077 pwnss 4078 elfir 6854 istopg 12155 uniopn 12157 iscld 12261 ntrval 12268 clsval 12269 discld 12294 neival 12301 isnei 12302 restdis 12342 cnpfval 12353 cndis 12399 blfvalps 12543 blfps 12567 blf 12568 reldvg 12806 |
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