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Mirrors > Home > ILE Home > Th. List > snelpw | Unicode version |
Description: A singleton of a set belongs to the power class of a class containing the set. (Contributed by NM, 1-Apr-1998.) |
Ref | Expression |
---|---|
snelpw.1 |
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Ref | Expression |
---|---|
snelpw |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snelpw.1 |
. . 3
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2 | 1 | snss 3494 |
. 2
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3 | snexgOLD 3935 |
. . . 4
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4 | 1, 3 | ax-mp 7 |
. . 3
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5 | 4 | elpw 3365 |
. 2
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6 | 2, 5 | bitr4i 176 |
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-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 |
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 df-sn 3381 |
This theorem is referenced by: (None) |
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