Step | Hyp | Ref
| Expression |
1 | | dedekindicc.a |
. . 3
   |
2 | | dedekindicc.b |
. . 3
   |
3 | | dedekindicc.lss |
. . 3

  ![[,] [,]](_icc.gif)    |
4 | | dedekindicc.uss |
. . 3

  ![[,] [,]](_icc.gif)    |
5 | | dedekindicc.lm |
. . 3
    ![[,] [,]](_icc.gif)     |
6 | | dedekindicc.um |
. . 3
    ![[,] [,]](_icc.gif)     |
7 | | dedekindicc.lr |
. . 3
    ![[,] [,]](_icc.gif)        |
8 | | dedekindicc.ur |
. . 3
    ![[,] [,]](_icc.gif)        |
9 | | dedekindicc.disj |
. . 3
     |
10 | | dedekindicc.loc |
. . 3
    ![[,] [,]](_icc.gif)      ![[,] [,]](_icc.gif)    
    |
11 | | dedekindicc.ab |
. . 3
   |
12 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11 | dedekindicclemlu 13775 |
. 2
    ![[,] [,]](_icc.gif)         |
13 | 1 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

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  #     |
14 | 2 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    
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15 | 3 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    
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  #     ![[,] [,]](_icc.gif)    |
16 | 4 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

     
  #     ![[,] [,]](_icc.gif)    |
17 | 5 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    
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)"   |
18 | 6 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    
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  #      ![[,] [,]](_icc.gif)     |
19 | 7 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

     
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)"      |
20 | 8 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

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  #      ![[,] [,]](_icc.gif)        |
21 | 9 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

     
  #       |
22 | 10 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

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  #      ![[,] [,]](_icc.gif)      ![[,] [,]](_icc.gif)   

    |
23 | 11 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

     
  #     |
24 | | simprll 537 |
. . . . . . . . . . 11
 
    ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)     
     ![[,] [,]](_icc.gif)    |
25 | 24 | ad3antrrr 492 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

     
  #     ![[,] [,]](_icc.gif)    |
26 | | simprr 531 |
. . . . . . . . . . 11
 
    ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)     
    
    |
27 | 26 | ad3antrrr 492 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

     
  #    

   |
28 | | simprlr 538 |
. . . . . . . . . . 11
 
    ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)     
     ![[,] [,]](_icc.gif)    |
29 | 28 | ad3antrrr 492 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    
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)"  |
30 | | simpllr 534 |
. . . . . . . . . 10
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  ![[,] [,]](_icc.gif)    
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31 | | simpr 110 |
. . . . . . . . . 10
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  ![[,] [,]](_icc.gif)    
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  #     |
32 | 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 27, 29, 30, 31 | dedekindicclemeu 13776 |
. . . . . . . . 9
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  ![[,] [,]](_icc.gif)    
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33 | 1 | ad4antr 494 |
. . . . . . . . . 10
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  ![[,] [,]](_icc.gif)    
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  #     |
34 | 2 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    
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  #     |
35 | 3 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    
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     
  #     ![[,] [,]](_icc.gif)    |
36 | 4 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

     
  #     ![[,] [,]](_icc.gif)    |
37 | 5 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    
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)"   |
38 | 6 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    
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)"   |
39 | 7 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

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  #      ![[,] [,]](_icc.gif)        |
40 | 8 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    
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     
  #      ![[,] [,]](_icc.gif)        |
41 | 9 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

     
  #       |
42 | 10 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

     
  #      ![[,] [,]](_icc.gif)      ![[,] [,]](_icc.gif)   

    |
43 | 11 | ad4antr 494 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

     
  #     |
44 | 28 | ad3antrrr 492 |
. . . . . . . . . 10
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  ![[,] [,]](_icc.gif)    
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)"  |
45 | | simpllr 534 |
. . . . . . . . . 10
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   |
46 | 24 | ad3antrrr 492 |
. . . . . . . . . 10
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  ![[,] [,]](_icc.gif)    
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)"  |
47 | 26 | ad3antrrr 492 |
. . . . . . . . . 10
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
   |
48 | | simpr 110 |
. . . . . . . . . 10
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

     
  #     |
49 | 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48 | dedekindicclemeu 13776 |
. . . . . . . . 9
         ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

     
  #    |
50 | | simpr 110 |
. . . . . . . . . 10
        ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

     
  #  #   |
51 | | iccssre 9942 |
. . . . . . . . . . . . . 14
 
   ![[,] [,]](_icc.gif) 
  |
52 | 1, 2, 51 | syl2anc 411 |
. . . . . . . . . . . . 13
   ![[,] [,]](_icc.gif) 
  |
53 | 52 | ad3antrrr 492 |
. . . . . . . . . . . 12
        ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

     
  #    ![[,] [,]](_icc.gif)    |
54 | 24 | ad2antrr 488 |
. . . . . . . . . . . 12
        ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    
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  #    ![[,] [,]](_icc.gif)    |
55 | 53, 54 | sseldd 3156 |
. . . . . . . . . . 11
        ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    
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     
  #    |
56 | 28 | ad2antrr 488 |
. . . . . . . . . . . 12
        ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

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)"  |
57 | 53, 56 | sseldd 3156 |
. . . . . . . . . . 11
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  ![[,] [,]](_icc.gif)    

     
  #    |
58 | | reaplt 8535 |
. . . . . . . . . . 11
 
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     |
59 | 55, 57, 58 | syl2anc 411 |
. . . . . . . . . 10
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  ![[,] [,]](_icc.gif)    
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     
  #   #
     |
60 | 50, 59 | mpbid 147 |
. . . . . . . . 9
        ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    
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  #  
   |
61 | 32, 49, 60 | mpjaodan 798 |
. . . . . . . 8
        ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)    

     
  #   |
62 | 61 | inegd 1372 |
. . . . . . 7
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)    

     
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#   |
63 | 52 | ad2antrr 488 |
. . . . . . . . . 10
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)    
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     
    ![[,] [,]](_icc.gif) 
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64 | 24 | adantr 276 |
. . . . . . . . . 10
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)    
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     
 
  ![[,] [,]](_icc.gif)    |
65 | 63, 64 | sseldd 3156 |
. . . . . . . . 9
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)    
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     
 
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66 | 65 | recnd 7976 |
. . . . . . . 8
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)    
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67 | 28 | adantr 276 |
. . . . . . . . . 10
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)    
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68 | 63, 67 | sseldd 3156 |
. . . . . . . . 9
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)    
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69 | 68 | recnd 7976 |
. . . . . . . 8
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)    
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70 | | apti 8569 |
. . . . . . . 8
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#    |
71 | 66, 69, 70 | syl2anc 411 |
. . . . . . 7
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)    
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("
#    |
72 | 62, 71 | mpbird 167 |
. . . . . 6
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)    
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73 | | ancom 266 |
. . . . . . . . . . . . . . 15
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74 | 73 | anbi2i 457 |
. . . . . . . . . . . . . 14
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75 | | anass 401 |
. . . . . . . . . . . . . 14
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)"  
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76 | 74, 75 | bitr4i 187 |
. . . . . . . . . . . . 13
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)   
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77 | 76 | anbi2i 457 |
. . . . . . . . . . . 12
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("
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("    ![[,] [,]](_icc.gif) 
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78 | | anass 401 |
. . . . . . . . . . . 12
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)   
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)" 
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79 | 77, 78 | bitr4i 187 |
. . . . . . . . . . 11
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("      ![[,] [,]](_icc.gif) 
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   |
80 | 79 | anbi1i 458 |
. . . . . . . . . 10
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)    
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("
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)   
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81 | | anass 401 |
. . . . . . . . . 10
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)" 
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82 | 80, 81 | bitri 184 |
. . . . . . . . 9
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)    
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)" 
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
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83 | | anass 401 |
. . . . . . . . . . . 12
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84 | 83 | bicomi 132 |
. . . . . . . . . . 11
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("  
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  ![[,] [,]](_icc.gif)        |
85 | 84 | anbi1i 458 |
. . . . . . . . . 10
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)   
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("      ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)    
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86 | | anass 401 |
. . . . . . . . . 10
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  ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)     
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  
     ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)     
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87 | 85, 86 | bitri 184 |
. . . . . . . . 9
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)   
   
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
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("  
  ![[,] [,]](_icc.gif) 
  ![[,] [,]](_icc.gif)     
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       |
88 | 82, 87 | bitri 184 |
. . . . . . . 8
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)    
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89 | | anass 401 |
. . . . . . . . . 10
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90 | | ancom 266 |
. . . . . . . . . . 11
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91 | 90 | anbi1i 458 |
. . . . . . . . . 10
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92 | 89, 91 | bitr3i 186 |
. . . . . . . . 9
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("  
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93 | 92 | anbi2i 457 |
. . . . . . . 8
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("  
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94 | 88, 93 | bitri 184 |
. . . . . . 7
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("   ![[,] [,]](_icc.gif)    ![[,] [,]](_icc.gif)    
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("      
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95 | 94 | imbi1i 238 |
. . . . . 6
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)" |
96 | 72, 95 | mpbi 145 |
. . . . 5
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97 | 96 | ex 115 |
. . . 4
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("  
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98 | 97 | ralrimivva 2559 |
. . 3
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99 | | breq2 4004 |
. . . . . 6
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100 | 99 | ralbidv 2477 |
. . . . 5
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101 | | breq1 4003 |
. . . . . 6
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102 | 101 | ralbidv 2477 |
. . . . 5
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103 | 100, 102 | anbi12d 473 |
. . . 4
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("   
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104 | 103 | rmo4 2930 |
. . 3
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)" |
105 | 98, 104 | sylibr 134 |
. 2
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106 | | reu5 2689 |
. 2
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107 | 12, 105, 106 | sylanbrc 417 |
1
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