Step | Hyp | Ref
| Expression |
1 | | xblss2.1 |
. . . . . 6
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2 | | xblss2.2 |
. . . . . 6
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3 | | xblss2.4 |
. . . . . 6
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4 | | elbl 13558 |
. . . . . 6
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R"    |
5 | 1, 2, 3, 4 | syl3anc 1238 |
. . . . 5
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)" 
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R"    |
6 | 5 | simprbda 383 |
. . . 4
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)"     |
7 | 1 | adantr 276 |
. . . . . . . 8
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)"  |
8 | | xblss2.3 |
. . . . . . . . 9
   |
9 | 8 | adantr 276 |
. . . . . . . 8
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)"     |
10 | | xmetcl 13519 |
. . . . . . . 8
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RR*"  |
11 | 7, 9, 6, 10 | syl3anc 1238 |
. . . . . . 7
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               |
12 | 11 | adantr 276 |
. . . . . 6
                   |
13 | | xblss2.6 |
. . . . . . . . . 10
       |
14 | 13 | adantr 276 |
. . . . . . . . 9
 
               |
15 | 14 | rexrd 7997 |
. . . . . . . 8
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               |
16 | 3 | adantr 276 |
. . . . . . . 8
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           |
17 | 15, 16 | xaddcld 9871 |
. . . . . . 7
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                    |
18 | 17 | adantr 276 |
. . . . . 6
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("          |
19 | | xblss2.5 |
. . . . . . 7
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20 | 19 | ad2antrr 488 |
. . . . . 6
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21 | 2 | adantr 276 |
. . . . . . . . . 10
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)"     |
22 | | xmetcl 13519 |
. . . . . . . . . 10
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RR*"  |
23 | 7, 21, 6, 22 | syl3anc 1238 |
. . . . . . . . 9
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)"         |
24 | 15, 23 | xaddcld 9871 |
. . . . . . . 8
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)"                  |
25 | | xmettri2 13528 |
. . . . . . . . 9
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26 | 7, 21, 9, 6, 25 | syl13anc 1240 |
. . . . . . . 8
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27 | 5 | simplbda 384 |
. . . . . . . . 9
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)" |
28 | | xltadd2 9864 |
. . . . . . . . . 10
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("            |
29 | 23, 16, 14, 28 | syl3anc 1238 |
. . . . . . . . 9
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)"                                 |
30 | 27, 29 | mpbid 147 |
. . . . . . . 8
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                                 |
31 | 11, 24, 17, 26, 30 | xrlelttrd 9797 |
. . . . . . 7
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)"                  |
32 | 31 | adantr 276 |
. . . . . 6
                            |
33 | 19 | adantr 276 |
. . . . . . . . . 10
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)"     |
34 | 16 | xnegcld 9842 |
. . . . . . . . . 10
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)"       |
35 | 33, 34 | xaddcld 9871 |
. . . . . . . . 9
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)"           |
36 | | xblss2.7 |
. . . . . . . . . 10
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37 | 36 | adantr 276 |
. . . . . . . . 9
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)"               |
38 | | xleadd1a 9860 |
. . . . . . . . 9
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("             |
39 | 15, 35, 16, 37, 38 | syl31anc 1241 |
. . . . . . . 8
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)"                         |
40 | 39 | adantr 276 |
. . . . . . 7
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("       
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R"       |
41 | | xnpcan 9859 |
. . . . . . . 8
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("            |
42 | 33, 41 | sylan 283 |
. . . . . . 7
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("            |
43 | 40, 42 | breqtrd 4026 |
. . . . . 6
                     
  |
44 | 12, 18, 20, 32, 43 | xrltletrd 9798 |
. . . . 5
                   |
45 | 27 | adantr 276 |
. . . . . 6
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R"  |
46 | 36 | ad2antrr 488 |
. . . . . . . . 9
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("        |
47 | 19 | ad2antrr 488 |
. . . . . . . . . . . . 13
               |
48 | | xrpnfdc 9829 |
. . . . . . . . . . . . 13
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DECID
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49 | 47, 48 | syl 14 |
. . . . . . . . . . . 12
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DECID
  |
50 | | 0xr 7994 |
. . . . . . . . . . . . . . . 16
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51 | 50 | a1i 9 |
. . . . . . . . . . . . . . 15
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           |
52 | | xmetge0 13532 |
. . . . . . . . . . . . . . . 16
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
      |
53 | 7, 21, 9, 52 | syl3anc 1238 |
. . . . . . . . . . . . . . 15
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               |
54 | 51, 15, 35, 53, 37 | xrletrd 9799 |
. . . . . . . . . . . . . 14
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)"           |
55 | | ge0nemnf 9811 |
. . . . . . . . . . . . . 14
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               |
56 | 35, 54, 55 | syl2anc 411 |
. . . . . . . . . . . . 13
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)"           |
57 | 56 | adantr 276 |
. . . . . . . . . . . 12
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R"   |
58 | | xaddmnf1 9835 |
. . . . . . . . . . . . . . . . 17
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59 | 58 | ex 115 |
. . . . . . . . . . . . . . . 16
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60 | 47, 59 | syl 14 |
. . . . . . . . . . . . . . 15
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61 | | simpr 110 |
. . . . . . . . . . . . . . . . . . 19
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62 | | xnegeq 9814 |
. . . . . . . . . . . . . . . . . . 19
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63 | 61, 62 | syl 14 |
. . . . . . . . . . . . . . . . . 18
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64 | | xnegpnf 9815 |
. . . . . . . . . . . . . . . . . 18
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65 | 63, 64 | eqtrdi 2226 |
. . . . . . . . . . . . . . . . 17
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66 | 65 | oveq2d 5885 |
. . . . . . . . . . . . . . . 16
                         |
67 | 66 | eqeq1d 2186 |
. . . . . . . . . . . . . . 15
                           |
68 | 60, 67 | sylibrd 169 |
. . . . . . . . . . . . . 14
             
         |
69 | 68 | a1d 22 |
. . . . . . . . . . . . 13
             DECID

  
       |
70 | 69 | necon1ddc 2425 |
. . . . . . . . . . . 12
             DECID
           |
71 | 49, 57, 70 | mp2d 47 |
. . . . . . . . . . 11
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72 | 71, 65 | oveq12d 5887 |
. . . . . . . . . 10
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R"      |
73 | | pnfaddmnf 9837 |
. . . . . . . . . 10
 
  |
74 | 72, 73 | eqtrdi 2226 |
. . . . . . . . 9
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R"   |
75 | 46, 74 | breqtrd 4026 |
. . . . . . . 8
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0"  |
76 | 53 | biantrud 304 |
. . . . . . . . . 10
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)"            
        |
77 | | xrletri3 9791 |
. . . . . . . . . . 11
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78 | 15, 50, 77 | sylancl 413 |
. . . . . . . . . 10
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)"            
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79 | | xmeteq0 13526 |
. . . . . . . . . . 11
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)"  |
80 | 7, 21, 9, 79 | syl3anc 1238 |
. . . . . . . . . 10
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)"       
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)"  |
81 | 76, 78, 80 | 3bitr2d 216 |
. . . . . . . . 9
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)"       
   |
82 | 81 | adantr 276 |
. . . . . . . 8
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("   
   |
83 | 75, 82 | mpbid 147 |
. . . . . . 7
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84 | 83 | oveq1d 5884 |
. . . . . 6
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85 | 61, 71 | eqtr4d 2213 |
. . . . . 6
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86 | 45, 84, 85 | 3brtr3d 4031 |
. . . . 5
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S"  |
87 | | xmetge0 13532 |
. . . . . . . . . . 11
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      |
88 | 7, 21, 6, 87 | syl3anc 1238 |
. . . . . . . . . 10
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)"         |
89 | 51, 23, 16, 88, 27 | xrlelttrd 9797 |
. . . . . . . . 9
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)"     |
90 | 51, 16, 89 | xrltled 9786 |
. . . . . . . 8
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)" |
91 | | ge0nemnf 9811 |
. . . . . . . 8
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92 | 16, 90, 91 | syl2anc 411 |
. . . . . . 7
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)"     |
93 | 16, 92 | jca 306 |
. . . . . 6
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)"   
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94 | | xrnemnf 9764 |
. . . . . 6
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95 | 93, 94 | sylib 122 |
. . . . 5
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)"       |
96 | 44, 86, 95 | mpjaodan 798 |
. . . 4
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)"         |
97 | | elbl 13558 |
. . . . 5
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S"    |
98 | 7, 9, 33, 97 | syl3anc 1238 |
. . . 4
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99 | 6, 96, 98 | mpbir2and 944 |
. . 3
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100 | 99 | ex 115 |
. 2
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101 | 100 | ssrdv 3161 |
1
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