Proof of Theorem elfzodifsumelfzo
Step | Hyp | Ref
| Expression |
1 | | elfz2nn0 10098 |
. . 3
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2 | | elfz2nn0 10098 |
. . . . 5
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3 | | elfzo0 10168 |
. . . . . . . 8
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4 | | nn0z 9262 |
. . . . . . . . . . . . 13
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5 | | nn0z 9262 |
. . . . . . . . . . . . 13
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6 | | znnsub 9293 |
. . . . . . . . . . . . 13
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7 | 4, 5, 6 | syl2an 289 |
. . . . . . . . . . . 12
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("      |
8 | | simpr 110 |
. . . . . . . . . . . . . . . 16
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9 | | simpll 527 |
. . . . . . . . . . . . . . . 16
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10 | | nn0addcl 9200 |
. . . . . . . . . . . . . . . 16
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("    |
11 | 8, 9, 10 | syl2anr 290 |
. . . . . . . . . . . . . . 15
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12 | 11 | adantr 276 |
. . . . . . . . . . . . . 14
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13 | | 0red 7949 |
. . . . . . . . . . . . . . . . . . . . . 22
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14 | | nn0re 9174 |
. . . . . . . . . . . . . . . . . . . . . . 23
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15 | 14 | adantr 276 |
. . . . . . . . . . . . . . . . . . . . . 22
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16 | | nn0re 9174 |
. . . . . . . . . . . . . . . . . . . . . . 23
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17 | 16 | adantl 277 |
. . . . . . . . . . . . . . . . . . . . . 22
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18 | 13, 15, 17 | 3jca 1177 |
. . . . . . . . . . . . . . . . . . . . 21
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("
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)" |
19 | 18 | adantr 276 |
. . . . . . . . . . . . . . . . . . . 20
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     |
20 | | nn0ge0 9190 |
. . . . . . . . . . . . . . . . . . . . . 22
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21 | 20 | adantr 276 |
. . . . . . . . . . . . . . . . . . . . 21
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22 | 21 | anim1i 340 |
. . . . . . . . . . . . . . . . . . . 20
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     |
23 | | lelttr 8036 |
. . . . . . . . . . . . . . . . . . . 20
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("
    |
24 | 19, 22, 23 | sylc 62 |
. . . . . . . . . . . . . . . . . . 19
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   |
25 | 24 | ex 115 |
. . . . . . . . . . . . . . . . . 18
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("    |
26 | | 0red 7949 |
. . . . . . . . . . . . . . . . . . . . . . . . 25
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27 | 16 | adantl 277 |
. . . . . . . . . . . . . . . . . . . . . . . . 25
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28 | | nn0re 9174 |
. . . . . . . . . . . . . . . . . . . . . . . . . 26
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29 | 28 | adantr 276 |
. . . . . . . . . . . . . . . . . . . . . . . . 25
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30 | | ltletr 8037 |
. . . . . . . . . . . . . . . . . . . . . . . . 25
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("
   
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32 | | nn0z 9262 |
. . . . . . . . . . . . . . . . . . . . . . . . . 26
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  |
33 | | elnnz 9252 |
. . . . . . . . . . . . . . . . . . . . . . . . . . 27

    |
34 | 33 | simplbi2 385 |
. . . . . . . . . . . . . . . . . . . . . . . . . 26
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35 | 32, 34 | syl 14 |
. . . . . . . . . . . . . . . . . . . . . . . . 25
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    |
36 | 35 | adantr 276 |
. . . . . . . . . . . . . . . . . . . . . . . 24
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("    |
37 | 31, 36 | syld 45 |
. . . . . . . . . . . . . . . . . . . . . . 23
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(" 
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   |
38 | 37 | exp4b 367 |
. . . . . . . . . . . . . . . . . . . . . 22
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39 | 38 | com24 87 |
. . . . . . . . . . . . . . . . . . . . 21
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      |
40 | 39 | imp 124 |
. . . . . . . . . . . . . . . . . . . 20
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("      |
41 | 40 | com13 80 |
. . . . . . . . . . . . . . . . . . 19
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("
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42 | 41 | adantl 277 |
. . . . . . . . . . . . . . . . . 18
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("  
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43 | 25, 42 | syld 45 |
. . . . . . . . . . . . . . . . 17
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("  
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44 | 43 | imp 124 |
. . . . . . . . . . . . . . . 16
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45 | 44 | adantr 276 |
. . . . . . . . . . . . . . 15
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N" 
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(" 
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46 | 45 | imp 124 |
. . . . . . . . . . . . . 14
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NN0"  
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  |
47 | | nn0re 9174 |
. . . . . . . . . . . . . . . . . . . . 21
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  |
48 | 47 | adantl 277 |
. . . . . . . . . . . . . . . . . . . 20
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49 | 15 | adantr 276 |
. . . . . . . . . . . . . . . . . . . 20
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50 | | readdcl 7928 |
. . . . . . . . . . . . . . . . . . . 20
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51 | 48, 49, 50 | syl2anr 290 |
. . . . . . . . . . . . . . . . . . 19
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N" 
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("    |
52 | 51 | adantr 276 |
. . . . . . . . . . . . . . . . . 18
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  
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("    |
53 | 17 | adantr 276 |
. . . . . . . . . . . . . . . . . . . 20
   
   |
54 | 53 | adantr 276 |
. . . . . . . . . . . . . . . . . . 19
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  
   
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55 | 54 | adantr 276 |
. . . . . . . . . . . . . . . . . 18
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NN0"  
   
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56 | 28 | adantl 277 |
. . . . . . . . . . . . . . . . . 18
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  
   
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57 | 52, 55, 56 | 3jca 1177 |
. . . . . . . . . . . . . . . . 17
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NN0"  
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("  
   |
58 | 57 | adantr 276 |
. . . . . . . . . . . . . . . 16
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59 | 47 | adantl 277 |
. . . . . . . . . . . . . . . . . . . . . . . 24
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60 | 15 | adantr 276 |
. . . . . . . . . . . . . . . . . . . . . . . 24
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61 | 17 | adantr 276 |
. . . . . . . . . . . . . . . . . . . . . . . 24
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62 | 59, 60, 61 | ltaddsubd 8492 |
. . . . . . . . . . . . . . . . . . . . . . 23
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63 | 62 | exbiri 382 |
. . . . . . . . . . . . . . . . . . . . . 22
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("  
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)"  |
64 | 63 | com23 78 |
. . . . . . . . . . . . . . . . . . . . 21
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)"  |
65 | 64 | impd 254 |
. . . . . . . . . . . . . . . . . . . 20
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)"  |
66 | 65 | adantr 276 |
. . . . . . . . . . . . . . . . . . 19
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           |
67 | 66 | imp 124 |
. . . . . . . . . . . . . . . . . 18
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N" 
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(" 
  |
68 | 67 | adantr 276 |
. . . . . . . . . . . . . . . . 17
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69 | 68 | anim1i 340 |
. . . . . . . . . . . . . . . 16
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70 | | ltletr 8037 |
. . . . . . . . . . . . . . . 16
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71 | 58, 69, 70 | sylc 62 |
. . . . . . . . . . . . . . 15
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72 | 71 | anasss 399 |
. . . . . . . . . . . . . 14
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73 | | elfzo0 10168 |
. . . . . . . . . . . . . 14
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74 | 12, 46, 72, 73 | syl3anbrc 1181 |
. . . . . . . . . . . . 13
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75 | 74 | exp53 377 |
. . . . . . . . . . . 12
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76 | 7, 75 | sylbird 170 |
. . . . . . . . . . 11
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77 | 76 | 3adant3 1017 |
. . . . . . . . . 10
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78 | 77 | com14 88 |
. . . . . . . . 9
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79 | 78 | 3imp 1193 |
. . . . . . . 8
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80 | 3, 79 | sylbi 121 |
. . . . . . 7
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81 | 80 | com13 80 |
. . . . . 6
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82 | 81 | 3adant1 1015 |
. . . . 5
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83 | 2, 82 | sylbi 121 |
. . . 4
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84 | 83 | com12 30 |
. . 3
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85 | 1, 84 | sylbi 121 |
. 2
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86 | 85 | imp 124 |
1
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