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Mirrors > Home > ILE Home > Th. List > pw1ne3 | Unicode version |
Description: The power set of ![]() |
Ref | Expression |
---|---|
pw1ne3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1lt2o 6437 |
. . . . 5
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2 | ssnel 4565 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 1, 2 | mt2 640 |
. . . 4
![]() ![]() ![]() ![]() ![]() |
4 | 2onn 6516 |
. . . . . 6
![]() ![]() ![]() ![]() | |
5 | 4 | elexi 2749 |
. . . . 5
![]() ![]() ![]() ![]() |
6 | 5 | elpw 3580 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | 3, 6 | mtbir 671 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() |
8 | 5 | sucid 4414 |
. . . . 5
![]() ![]() ![]() ![]() ![]() |
9 | df-3o 6413 |
. . . . 5
![]() ![]() ![]() ![]() ![]() | |
10 | 8, 9 | eleqtrri 2253 |
. . . 4
![]() ![]() ![]() ![]() |
11 | eleq2 2241 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
12 | 10, 11 | mpbiri 168 |
. . 3
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13 | 7, 12 | mto 662 |
. 2
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14 | 13 | 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 4118 ax-nul 4126 ax-pow 4171 ax-pr 4206 ax-un 4430 ax-setind 4533 |
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 3576 df-sn 3597 df-pr 3598 df-uni 3808 df-int 3843 df-tr 4099 df-iord 4363 df-on 4365 df-suc 4368 df-iom 4587 df-1o 6411 df-2o 6412 df-3o 6413 |
This theorem is referenced by: 3nelsucpw1 7227 |
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