Proof of Theorem dfphi2
Step | Hyp | Ref
| Expression |
1 | | elnn1uz2 9596 |
. 2
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2 | | phi1 12202 |
. . . . 5
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3 | | 0z 9253 |
. . . . . 6
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4 | | hashsng 10762 |
. . . . . 6
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5 | 3, 4 | ax-mp 5 |
. . . . 5
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6 | | rabid2 2653 |
. . . . . . 7
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7 | | elsni 3609 |
. . . . . . . . 9
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8 | 7 | oveq1d 5884 |
. . . . . . . 8
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9 | | gcd1 11971 |
. . . . . . . . 9
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10 | 3, 9 | ax-mp 5 |
. . . . . . . 8
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11 | 8, 10 | eqtrdi 2226 |
. . . . . . 7
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12 | 6, 11 | mprgbir 2535 |
. . . . . 6
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13 | 12 | fveq2i 5514 |
. . . . 5
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14 | 2, 5, 13 | 3eqtr2i 2204 |
. . . 4
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15 | | fveq2 5511 |
. . . 4
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16 | | oveq2 5877 |
. . . . . . 7
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17 | | fzo01 10202 |
. . . . . . 7
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18 | 16, 17 | eqtrdi 2226 |
. . . . . 6
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19 | | oveq2 5877 |
. . . . . . 7
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20 | 19 | eqeq1d 2186 |
. . . . . 6
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21 | 18, 20 | rabeqbidv 2732 |
. . . . 5
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22 | 21 | fveq2d 5515 |
. . . 4
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23 | 14, 15, 22 | 3eqtr4a 2236 |
. . 3
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24 | | eluz2nn 9555 |
. . . . 5
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25 | | phival 12196 |
. . . . 5
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26 | 24, 25 | syl 14 |
. . . 4
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27 | | fzossfz 10151 |
. . . . . . . . . . 11
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1"    |
28 | 27 | a1i 9 |
. . . . . . . . . 10
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1"     |
29 | | sseqin2 3354 |
. . . . . . . . . 10
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30 | 28, 29 | sylib 122 |
. . . . . . . . 9
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1"    ..^   ..^   |
31 | | fzo0ss1 10160 |
. . . . . . . . . 10
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32 | | sseqin2 3354 |
. . . . . . . . . 10
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  ..^  ..^   ..^   |
33 | 31, 32 | mpbi 145 |
. . . . . . . . 9
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34 | 30, 33 | eqtr4di 2228 |
. . . . . . . 8
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1"    ..^    ..^  ..^    |
35 | 34 | rabeqdv 2731 |
. . . . . . 7
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36 | | inrab2 3408 |
. . . . . . 7
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37 | | inrab2 3408 |
. . . . . . 7
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38 | 35, 36, 37 | 3eqtr4g 2235 |
. . . . . 6
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39 | | phibndlem 12199 |
. . . . . . . 8
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1"    |
40 | | eluzelz 9526 |
. . . . . . . . 9
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41 | | fzoval 10134 |
. . . . . . . . 9
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    |
42 | 40, 41 | syl 14 |
. . . . . . . 8
    
 ..^         |
43 | 39, 42 | sseqtrrd 3194 |
. . . . . . 7
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44 | | df-ss 3142 |
. . . . . . 7
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45 | 43, 44 | sylib 122 |
. . . . . 6
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46 | | gcd0id 11963 |
. . . . . . . . . . . . . . . 16
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       |
47 | 40, 46 | syl 14 |
. . . . . . . . . . . . . . 15
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48 | | eluzelre 9527 |
. . . . . . . . . . . . . . . 16
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49 | | eluzge2nn0 9558 |
. . . . . . . . . . . . . . . . 17
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50 | 49 | nn0ge0d 9221 |
. . . . . . . . . . . . . . . 16
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51 | 48, 50 | absidd 11160 |
. . . . . . . . . . . . . . 15
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52 | 47, 51 | eqtrd 2210 |
. . . . . . . . . . . . . 14
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53 | | eluz2b3 9593 |
. . . . . . . . . . . . . . 15
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54 | 53 | simprbi 275 |
. . . . . . . . . . . . . 14
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55 | 52, 54 | eqnetrd 2371 |
. . . . . . . . . . . . 13
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56 | 55 | adantr 276 |
. . . . . . . . . . . 12
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2"  ..^ 
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57 | 7 | oveq1d 5884 |
. . . . . . . . . . . . . 14
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58 | 57, 17 | eleq2s 2272 |
. . . . . . . . . . . . 13
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59 | 58 | neeq1d 2365 |
. . . . . . . . . . . 12
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N"    |
60 | 56, 59 | syl5ibrcom 157 |
. . . . . . . . . . 11
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2"  ..^ 
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61 | 60 | necon2bd 2405 |
. . . . . . . . . 10
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62 | | simpr 110 |
. . . . . . . . . . . 12
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2"  ..^ 
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63 | | 1z 9268 |
. . . . . . . . . . . 12
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64 | | fzospliti 10162 |
. . . . . . . . . . . 12
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65 | 62, 63, 64 | sylancl 413 |
. . . . . . . . . . 11
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2"  ..^ 
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66 | 65 | ord 724 |
. . . . . . . . . 10
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2"  ..^ 
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67 | 61, 66 | syld 45 |
. . . . . . . . 9
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68 | 67 | ralrimiva 2550 |
. . . . . . . 8
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69 | | rabss 3232 |
. . . . . . . 8
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70 | 68, 69 | sylibr 134 |
. . . . . . 7
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71 | | df-ss 3142 |
. . . . . . 7
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72 | 70, 71 | sylib 122 |
. . . . . 6
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73 | 38, 45, 72 | 3eqtr3d 2218 |
. . . . 5
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74 | 73 | fveq2d 5515 |
. . . 4
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75 | 26, 74 | eqtrd 2210 |
. . 3
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76 | 23, 75 | jaoi 716 |
. 2
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77 | 1, 76 | sylbi 121 |
1
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