Step | Hyp | Ref
| Expression |
1 | | df-nqqs 7338 |
. . . . . 6
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2 | | id 19 |
. . . . . . . 8
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3 | 2, 2 | breq12d 4013 |
. . . . . . 7
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4 | 3 | notbid 667 |
. . . . . 6
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5 | | ltsopi 7310 |
. . . . . . . 8
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6 | | ltrelpi 7314 |
. . . . . . . 8
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7 | 5, 6 | soirri 5019 |
. . . . . . 7
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8 | | ordpipqqs 7364 |
. . . . . . . . 9
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9 | 8 | anidms 397 |
. . . . . . . 8
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10 | | mulcompig 7321 |
. . . . . . . . 9
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11 | 10 | breq1d 4010 |
. . . . . . . 8
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12 | 9, 11 | bitrd 188 |
. . . . . . 7
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13 | 7, 12 | mtbiri 675 |
. . . . . 6
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14 | 1, 4, 13 | ecoptocl 6616 |
. . . . 5
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15 | 14 | adantl 277 |
. . . 4
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16 | | breq1 4003 |
. . . . . . . 8
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>."
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17 | 16 | anbi1d 465 |
. . . . . . 7
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18 | | breq1 4003 |
. . . . . . 7
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19 | 17, 18 | imbi12d 234 |
. . . . . 6
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20 | | breq2 4004 |
. . . . . . . 8
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21 | | breq1 4003 |
. . . . . . . 8
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>."
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22 | 20, 21 | anbi12d 473 |
. . . . . . 7
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23 | 22 | imbi1d 231 |
. . . . . 6
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24 | | breq2 4004 |
. . . . . . . 8
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25 | 24 | anbi2d 464 |
. . . . . . 7
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26 | | breq2 4004 |
. . . . . . 7
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("         |
27 | 25, 26 | imbi12d 234 |
. . . . . 6
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28 | | ordpipqqs 7364 |
. . . . . . . . . . . . . . . 16
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29 | 28 | 3adant3 1017 |
. . . . . . . . . . . . . . 15
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30 | | simp1l 1021 |
. . . . . . . . . . . . . . . . 17
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31 | | simp2r 1024 |
. . . . . . . . . . . . . . . . 17
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32 | | mulclpi 7318 |
. . . . . . . . . . . . . . . . 17
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33 | 30, 31, 32 | syl2anc 411 |
. . . . . . . . . . . . . . . 16
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34 | | simp1r 1022 |
. . . . . . . . . . . . . . . . 17
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35 | | simp2l 1023 |
. . . . . . . . . . . . . . . . 17
        
  |
36 | | mulclpi 7318 |
. . . . . . . . . . . . . . . . 17
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     |
37 | 34, 35, 36 | syl2anc 411 |
. . . . . . . . . . . . . . . 16
        
    |
38 | | simp3r 1026 |
. . . . . . . . . . . . . . . . 17
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39 | | mulclpi 7318 |
. . . . . . . . . . . . . . . . 17
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     |
40 | 35, 38, 39 | syl2anc 411 |
. . . . . . . . . . . . . . . 16
        
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41 | | ltmpig 7329 |
. . . . . . . . . . . . . . . 16
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("     
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42 | 33, 37, 40, 41 | syl3anc 1238 |
. . . . . . . . . . . . . . 15
        
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("        |
43 | 29, 42 | bitrd 188 |
. . . . . . . . . . . . . 14
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44 | 43 | biimpa 296 |
. . . . . . . . . . . . 13
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45 | 44 | adantrr 479 |
. . . . . . . . . . . 12
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("             |
46 | | mulcompig 7321 |
. . . . . . . . . . . . . 14
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47 | 40, 37, 46 | syl2anc 411 |
. . . . . . . . . . . . 13
        
              |
48 | 47 | adantr 276 |
. . . . . . . . . . . 12
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["                         |
49 | 45, 48 | breqtrd 4026 |
. . . . . . . . . . 11
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50 | | ordpipqqs 7364 |
. . . . . . . . . . . . . . 15
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51 | 50 | 3adant1 1015 |
. . . . . . . . . . . . . 14
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52 | | simp3l 1025 |
. . . . . . . . . . . . . . . 16
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53 | | mulclpi 7318 |
. . . . . . . . . . . . . . . 16
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54 | 31, 52, 53 | syl2anc 411 |
. . . . . . . . . . . . . . 15
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55 | | ltmpig 7329 |
. . . . . . . . . . . . . . 15
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56 | 40, 54, 37, 55 | syl3anc 1238 |
. . . . . . . . . . . . . 14
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("        |
57 | 51, 56 | bitrd 188 |
. . . . . . . . . . . . 13
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58 | 57 | biimpa 296 |
. . . . . . . . . . . 12
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59 | 58 | adantrl 478 |
. . . . . . . . . . 11
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60 | 5, 6 | sotri 5020 |
. . . . . . . . . . 11
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61 | 49, 59, 60 | syl2anc 411 |
. . . . . . . . . 10
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62 | | mulcompig 7321 |
. . . . . . . . . . . . . . 15
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63 | 62 | adantl 277 |
. . . . . . . . . . . . . 14
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N."     |
65 | 64 | adantl 277 |
. . . . . . . . . . . . . 14
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("         |
66 | | mulclpi 7318 |
. . . . . . . . . . . . . . 15
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67 | 66 | adantl 277 |
. . . . . . . . . . . . . 14
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N."      |
68 | 35, 31, 30, 63, 65, 38, 67 | caov411d 6054 |
. . . . . . . . . . . . 13
        
              |
69 | 63, 33, 40 | caovcomd 6025 |
. . . . . . . . . . . . 13
        
              |
70 | 68, 69 | eqtrd 2210 |
. . . . . . . . . . . 12
        
              |
71 | 35, 31, 34, 63, 65, 52, 67 | caov4d 6053 |
. . . . . . . . . . . . 13
        
              |
72 | 63, 35, 34 | caovcomd 6025 |
. . . . . . . . . . . . . 14
        
      |
73 | 72 | oveq1d 5884 |
. . . . . . . . . . . . 13
        
              |
74 | 71, 73 | eqtrd 2210 |
. . . . . . . . . . . 12
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75 | 70, 74 | breq12d 4013 |
. . . . . . . . . . 11
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("                          |
76 | 75 | adantr 276 |
. . . . . . . . . 10
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["                 
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("         |
77 | 61, 76 | mpbird 167 |
. . . . . . . . 9
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["                         |
78 | | mulclpi 7318 |
. . . . . . . . . . . 12
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     |
79 | 30, 38, 78 | syl2anc 411 |
. . . . . . . . . . 11
        
    |
80 | | mulclpi 7318 |
. . . . . . . . . . . 12
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     |
81 | 34, 52, 80 | syl2anc 411 |
. . . . . . . . . . 11
        
    |
82 | | mulclpi 7318 |
. . . . . . . . . . . 12
 
     |
83 | 35, 31, 82 | syl2anc 411 |
. . . . . . . . . . 11
        
    |
84 | | ltmpig 7329 |
. . . . . . . . . . 11
                   
         |
85 | 79, 81, 83, 84 | syl3anc 1238 |
. . . . . . . . . 10
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86 | 85 | adantr 276 |
. . . . . . . . 9
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87 | 77, 86 | mpbird 167 |
. . . . . . . 8
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88 | | ordpipqqs 7364 |
. . . . . . . . . 10
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)"   |
89 | 88 | 3adant2 1016 |
. . . . . . . . 9
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)"   |
90 | 89 | adantr 276 |
. . . . . . . 8
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>."             |
91 | 87, 90 | mpbird 167 |
. . . . . . 7
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92 | 91 | ex 115 |
. . . . . 6
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93 | 1, 19, 23, 27, 92 | 3ecoptocl 6618 |
. . . . 5
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94 | 93 | adantl 277 |
. . . 4
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95 | 15, 94 | ispod 4301 |
. . 3
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96 | | nqtri3or 7386 |
. . . 4
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97 | 96 | adantl 277 |
. . 3
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98 | 95, 97 | issod 4316 |
. 2
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99 | 98 | mptru 1362 |
1
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