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Mirrors > Home > ILE Home > Th. List > pw1ne1 | Unicode version |
Description: The power set of ![]() |
Ref | Expression |
---|---|
pw1ne1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pw1on 7224 |
. . . 4
![]() ![]() ![]() ![]() ![]() | |
2 | 1 | onirri 4542 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | df1o2 6429 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() | |
4 | pwpw0ss 3804 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 3 | pweqi 3579 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | 4, 5 | sseqtrri 3190 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | 0ex 4130 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
8 | p0ex 4188 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 7, 8 | prss 3748 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | 6, 9 | mpbir 146 |
. . . . . 6
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11 | 10 | simpri 113 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
12 | 3, 11 | eqeltri 2250 |
. . . 4
![]() ![]() ![]() ![]() ![]() |
13 | eleq1 2240 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
14 | 12, 13 | mpbiri 168 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 2, 14 | mto 662 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() |
16 | 15 | neir 2350 |
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-in1 614 ax-in2 615 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-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-nul 4129 ax-pow 4174 ax-pr 4209 ax-un 4433 ax-setind 4536 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-pw 3577 df-sn 3598 df-pr 3599 df-uni 3810 df-tr 4102 df-iord 4366 df-on 4368 df-suc 4371 df-1o 6416 |
This theorem is referenced by: pw1nel3 7229 sucpw1nel3 7231 |
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