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Mirrors > Home > NFE Home > Th. List > dfpw12 | Unicode version |
Description: Alternate expression for unit power classes. (Contributed by SF, 26-Jan-2015.) |
Ref | Expression |
---|---|
dfpw12 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elpw1 4145 |
. . 3
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2 | vex 2863 |
. . . . 5
![]() ![]() ![]() ![]() | |
3 | 2 | elimakv 4261 |
. . . 4
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4 | vex 2863 |
. . . . . . 7
![]() ![]() ![]() ![]() | |
5 | opkelsikg 4265 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | 4, 2, 5 | mp2an 653 |
. . . . . 6
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7 | 6 | exbii 1582 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | exrot3 1744 |
. . . . 5
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9 | 7, 8 | bitr4i 243 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | df-3an 936 |
. . . . . . . . 9
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11 | vex 2863 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() | |
12 | vex 2863 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() | |
13 | 11, 12 | opkelxpk 4249 |
. . . . . . . . . 10
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14 | 13 | anbi2i 675 |
. . . . . . . . 9
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15 | an4 797 |
. . . . . . . . 9
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16 | 10, 14, 15 | 3bitri 262 |
. . . . . . . 8
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17 | 16 | 2exbii 1583 |
. . . . . . 7
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18 | 19.41vv 1902 |
. . . . . . 7
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19 | sneq 3745 |
. . . . . . . . . . . 12
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20 | eqeq12 2365 |
. . . . . . . . . . . 12
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21 | 19, 20 | sylan2 460 |
. . . . . . . . . . 11
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22 | eleq1 2413 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
23 | 22 | adantl 452 |
. . . . . . . . . . 11
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24 | 21, 23 | anbi12d 691 |
. . . . . . . . . 10
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25 | 2, 12, 24 | spc2ev 2948 |
. . . . . . . . 9
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26 | 25 | pm4.71ri 614 |
. . . . . . . 8
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27 | ancom 437 |
. . . . . . . 8
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28 | 26, 27 | bitr3i 242 |
. . . . . . 7
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29 | 17, 18, 28 | 3bitri 262 |
. . . . . 6
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30 | 29 | exbii 1582 |
. . . . 5
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31 | df-rex 2621 |
. . . . 5
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32 | 30, 31 | bitr4i 243 |
. . . 4
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33 | 3, 9, 32 | 3bitri 262 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
34 | 1, 33 | bitr4i 243 |
. 2
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35 | 34 | eqriv 2350 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4079 ax-sn 4088 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-ne 2519 df-rex 2621 df-v 2862 df-nin 3212 df-compl 3213 df-in 3214 df-un 3215 df-dif 3216 df-ss 3260 df-nul 3552 df-pw 3725 df-sn 3742 df-pr 3743 df-opk 4059 df-1c 4137 df-pw1 4138 df-xpk 4186 df-imak 4190 df-sik 4193 |
This theorem is referenced by: pw1exg 4303 |
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