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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 3563 | . 2 | |
2 | ssexg 4116 | . . . 4 | |
3 | elpwg 3562 | . . . . 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 2135 cvv 2722 wss 3112 cpw 3554 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 ax-sep 4095 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2724 df-in 3118 df-ss 3125 df-pw 3556 |
This theorem is referenced by: elpw2 4131 pwnss 4133 ifelpwung 4454 elfir 6930 istopg 12564 uniopn 12566 iscld 12670 ntrval 12677 clsval 12678 discld 12703 neival 12710 isnei 12711 restdis 12751 cnpfval 12762 cndis 12808 blfvalps 12952 blfps 12976 blf 12977 reldvg 13215 |
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