Step | Hyp | Ref
| Expression |
1 | | algcvga.5 |
. . 3
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)" |
2 | | algcvga.3 |
. . . 4
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-->"  |
3 | 2 | ffvelcdmi 5646 |
. . 3
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`"    |
4 | 1, 3 | eqeltrid 2264 |
. 2
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5 | | nn0z 9262 |
. . . 4
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6 | | eluz1 9521 |
. . . . 5
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7 | | 2fveq3 5516 |
. . . . . . . . 9
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`"                |
8 | 7 | eqeq1d 2186 |
. . . . . . . 8
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9 | 8 | imbi2d 230 |
. . . . . . 7
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`"       |
10 | | 2fveq3 5516 |
. . . . . . . . 9
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)"  |
11 | 10 | eqeq1d 2186 |
. . . . . . . 8
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`"              |
12 | 11 | imbi2d 230 |
. . . . . . 7
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("                       |
13 | | 2fveq3 5516 |
. . . . . . . . 9
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`"                  |
14 | 13 | eqeq1d 2186 |
. . . . . . . 8
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("                     |
15 | 14 | imbi2d 230 |
. . . . . . 7
                             |
16 | | 2fveq3 5516 |
. . . . . . . . 9
                   |
17 | 16 | eqeq1d 2186 |
. . . . . . . 8
                     |
18 | 17 | imbi2d 230 |
. . . . . . 7
                         |
19 | | algcvga.1 |
. . . . . . . . 9
     |
20 | | algcvga.2 |
. . . . . . . . 9
            |
21 | | algcvga.4 |
. . . . . . . . 9
                 
       |
22 | 19, 20, 2, 21, 1 | algcvg 12031 |
. . . . . . . 8
           |
23 | 22 | a1i 9 |
. . . . . . 7
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24 | | nn0ge0 9190 |
. . . . . . . . . . . . . . . . 17
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25 | 24 | adantr 276 |
. . . . . . . . . . . . . . . 16
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26 | | nn0re 9174 |
. . . . . . . . . . . . . . . . 17
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27 | | zre 9246 |
. . . . . . . . . . . . . . . . 17
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28 | | 0re 7948 |
. . . . . . . . . . . . . . . . . 18
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29 | | letr 8030 |
. . . . . . . . . . . . . . . . . 18
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("
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)"  |
30 | 28, 29 | mp3an1 1324 |
. . . . . . . . . . . . . . . . 17
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31 | 26, 27, 30 | syl2an 289 |
. . . . . . . . . . . . . . . 16
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32 | 25, 31 | mpand 429 |
. . . . . . . . . . . . . . 15
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33 | | elnn0z 9255 |
. . . . . . . . . . . . . . . . 17
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k"   |
34 | 33 | simplbi2 385 |
. . . . . . . . . . . . . . . 16
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35 | 34 | adantl 277 |
. . . . . . . . . . . . . . 15
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36 | 32, 35 | syld 45 |
. . . . . . . . . . . . . 14
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37 | 4, 36 | sylan 283 |
. . . . . . . . . . . . 13
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)" |
38 | 37 | impr 379 |
. . . . . . . . . . . 12
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39 | 38 | expcom 116 |
. . . . . . . . . . 11
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("         |
48 | | 2fveq3 5516 |
. . . . . . . . . . . . . . 15
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`"         |
49 | 48 | neeq1d 2365 |
. . . . . . . . . . . . . 14
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("          |
50 | | fveq2 5511 |
. . . . . . . . . . . . . . 15
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51 | 48, 50 | breq12d 4013 |
. . . . . . . . . . . . . 14
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52 | 49, 51 | imbi12d 234 |
. . . . . . . . . . . . 13
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`"          |
53 | 52, 21 | vtoclga 2803 |
. . . . . . . . . . . 12
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54 | 19, 2 | algcvgb 12033 |
. . . . . . . . . . . . 13
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55 | | simpr 110 |
. . . . . . . . . . . . 13
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`"       |
56 | 54, 55 | syl6bi 163 |
. . . . . . . . . . . 12
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`"                                 |
57 | 53, 56 | mpd 13 |
. . . . . . . . . . 11
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("                       |
58 | 47, 57 | syl 14 |
. . . . . . . . . 10
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("                        |
59 | 42, 20, 43, 44, 45 | algrp1 12029 |
. . . . . . . . . . 11
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("                |
60 | 59 | fveqeq2d 5519 |
. . . . . . . . . 10
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`"             |
61 | 58, 60 | sylibrd 169 |
. . . . . . . . 9
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("                      |
62 | 41, 61 | syl6 33 |
. . . . . . . 8
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`"                 |
63 | 62 | a2d 26 |
. . . . . . 7
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`"    
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64 | 9, 12, 15, 18, 23, 63 | uzind 9353 |
. . . . . 6
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65 | 64 | 3expib 1206 |
. . . . 5
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66 | 6, 65 | sylbid 150 |
. . . 4
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67 | 5, 66 | syl 14 |
. . 3
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68 | 67 | com3r 79 |
. 2
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69 | 4, 68 | mpd 13 |
1
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