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Mirrors > Home > ILE Home > Th. List > ordtri2or2exmidlem | Unicode version |
Description: A set which is ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
ordtri2or2exmidlem |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpll 519 |
. . . . . . 7
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2 | noel 3372 |
. . . . . . . . 9
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3 | eleq2 2204 |
. . . . . . . . 9
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4 | 2, 3 | mtbiri 665 |
. . . . . . . 8
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5 | 4 | adantl 275 |
. . . . . . 7
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6 | 1, 5 | pm2.21dd 610 |
. . . . . 6
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7 | eleq2 2204 |
. . . . . . . . . . 11
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8 | 7 | biimpac 296 |
. . . . . . . . . 10
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9 | velsn 3549 |
. . . . . . . . . 10
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10 | 8, 9 | sylib 121 |
. . . . . . . . 9
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11 | orc 702 |
. . . . . . . . . 10
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12 | vex 2692 |
. . . . . . . . . . 11
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13 | 12 | elpr 3553 |
. . . . . . . . . 10
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14 | 11, 13 | sylibr 133 |
. . . . . . . . 9
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15 | 10, 14 | syl 14 |
. . . . . . . 8
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16 | 15 | adantlr 469 |
. . . . . . 7
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17 | biidd 171 |
. . . . . . . . . 10
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18 | 17 | elrab 2844 |
. . . . . . . . 9
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19 | 18 | simprbi 273 |
. . . . . . . 8
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20 | 19 | ad2antlr 481 |
. . . . . . 7
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21 | biidd 171 |
. . . . . . . 8
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22 | 21 | elrab 2844 |
. . . . . . 7
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23 | 16, 20, 22 | sylanbrc 414 |
. . . . . 6
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24 | elrabi 2841 |
. . . . . . . 8
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25 | vex 2692 |
. . . . . . . . 9
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26 | 25 | elpr 3553 |
. . . . . . . 8
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27 | 24, 26 | sylib 121 |
. . . . . . 7
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28 | 27 | adantl 275 |
. . . . . 6
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29 | 6, 23, 28 | mpjaodan 788 |
. . . . 5
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30 | 29 | gen2 1427 |
. . . 4
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31 | dftr2 4036 |
. . . 4
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32 | 30, 31 | mpbir 145 |
. . 3
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33 | ssrab2 3187 |
. . 3
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34 | 2ordpr 4447 |
. . 3
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35 | trssord 4310 |
. . 3
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36 | 32, 33, 34, 35 | mp3an 1316 |
. 2
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37 | pp0ex 4121 |
. . . 4
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38 | 37 | rabex 4080 |
. . 3
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39 | 38 | elon 4304 |
. 2
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40 | 36, 39 | mpbir 145 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-nul 4062 ax-pow 4106 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-nul 3369 df-pw 3517 df-sn 3538 df-pr 3539 df-uni 3745 df-tr 4035 df-iord 4296 df-on 4298 df-suc 4301 |
This theorem is referenced by: ordtri2or2exmid 4494 |
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