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Mirrors > Home > ILE Home > Th. List > exmidontriimlem4 | Unicode version |
Description: Lemma for exmidontriim 7221. The induction step for the induction on
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Ref | Expression |
---|---|
exmidontriimlem4.a |
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exmidontriimlem4.b |
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exmidontriimlem4.em |
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exmidontriimlem4.h |
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Ref | Expression |
---|---|
exmidontriimlem4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq2 2241 |
. . 3
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2 | eqeq2 2187 |
. . 3
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3 | eleq1 2240 |
. . 3
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4 | 1, 2, 3 | 3orbi123d 1311 |
. 2
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5 | eleq2w 2239 |
. . . . . . 7
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6 | eqeq2 2187 |
. . . . . . 7
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7 | eleq1w 2238 |
. . . . . . 7
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8 | 5, 6, 7 | 3orbi123d 1311 |
. . . . . 6
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9 | 8 | imbi2d 230 |
. . . . 5
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10 | exmidontriimlem4.a |
. . . . . . . 8
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11 | 10 | adantl 277 |
. . . . . . 7
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12 | simpll 527 |
. . . . . . 7
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13 | exmidontriimlem4.em |
. . . . . . . 8
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14 | 13 | adantl 277 |
. . . . . . 7
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15 | exmidontriimlem4.h |
. . . . . . . 8
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16 | 15 | adantl 277 |
. . . . . . 7
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17 | simplr 528 |
. . . . . . . . . 10
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18 | eleq2w 2239 |
. . . . . . . . . . . . 13
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19 | eqeq2 2187 |
. . . . . . . . . . . . 13
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20 | eleq1w 2238 |
. . . . . . . . . . . . 13
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21 | 18, 19, 20 | 3orbi123d 1311 |
. . . . . . . . . . . 12
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22 | 21 | imbi2d 230 |
. . . . . . . . . . 11
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23 | simpllr 534 |
. . . . . . . . . . 11
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24 | simpr 110 |
. . . . . . . . . . 11
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25 | 22, 23, 24 | rspcdva 2846 |
. . . . . . . . . 10
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26 | 17, 25 | mpd 13 |
. . . . . . . . 9
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27 | 26 | ralrimiva 2550 |
. . . . . . . 8
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28 | eleq2w 2239 |
. . . . . . . . . 10
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29 | eqeq2 2187 |
. . . . . . . . . 10
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30 | eleq1w 2238 |
. . . . . . . . . 10
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31 | 28, 29, 30 | 3orbi123d 1311 |
. . . . . . . . 9
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32 | 31 | cbvralv 2703 |
. . . . . . . 8
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33 | 27, 32 | sylib 122 |
. . . . . . 7
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34 | 11, 12, 14, 16, 33 | exmidontriimlem3 7219 |
. . . . . 6
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35 | 34 | exp31 364 |
. . . . 5
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36 | 9, 35 | tfis2 4583 |
. . . 4
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37 | 36 | impcom 125 |
. . 3
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38 | 37 | ralrimiva 2550 |
. 2
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39 | exmidontriimlem4.b |
. 2
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40 | 4, 38, 39 | rspcdva 2846 |
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-14 2151 ax-ext 2159 ax-sep 4120 ax-nul 4128 ax-pow 4173 ax-setind 4535 |
This theorem depends on definitions: df-bi 117 df-dc 835 df-3or 979 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-dif 3131 df-in 3135 df-ss 3142 df-nul 3423 df-pw 3577 df-sn 3598 df-uni 3810 df-tr 4101 df-exmid 4194 df-iord 4365 df-on 4367 |
This theorem is referenced by: exmidontriim 7221 |
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