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Mirrors > Home > ILE Home > Th. List > elpwg | Unicode version |
Description: Membership in a power class. Theorem 86 of [Suppes] p. 47. (Contributed by NM, 6-Aug-2000.) |
Ref | Expression |
---|---|
elpwg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2100 |
. 2
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2 | sseq1 2966 |
. 2
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3 | vex 2560 |
. . 3
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4 | 3 | elpw 3365 |
. 2
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5 | 1, 2, 4 | vtoclbg 2614 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-in 2924 df-ss 2931 df-pw 3361 |
This theorem is referenced by: elpwi 3368 pwidg 3372 prsspwg 3523 elpw2g 3910 snelpwi 3948 prelpwi 3950 pwel 3954 eldifpw 4208 f1opw2 5706 2pwuninelg 5898 tfrlemibfn 5942 fopwdom 6310 |
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