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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 2240 |
. 2
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2 | sseq1 3178 |
. 2
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3 | vex 2740 |
. . 3
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4 | 3 | elpw 3580 |
. 2
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5 | 1, 2, 4 | vtoclbg 2798 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-in 3135 df-ss 3142 df-pw 3576 |
This theorem is referenced by: elpwi 3583 elpwb 3584 pwidg 3588 prsspwg 3750 elpw2g 4153 snelpwi 4208 prelpwi 4210 pwel 4214 eldifpw 4473 f1opw2 6070 2pwuninelg 6277 tfrlemibfn 6322 tfr1onlembfn 6338 tfrcllembfn 6351 elpmg 6657 fopwdom 6829 fiinopn 13135 ssntr 13255 |
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