Step | Hyp | Ref
| Expression |
1 | | euotd.1 |
. . . 4
   |
2 | | euotd.2 |
. . . 4
   |
3 | | euotd.3 |
. . . 4
   |
4 | | otexg 4227 |
. . . 4
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   
   |
5 | 1, 2, 3, 4 | syl3anc 1238 |
. . 3
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<."      |
6 | | euotd.4 |
. . . . . . . . . . . . 13
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    |
7 | 6 | biimpa 296 |
. . . . . . . . . . . 12
 
     |
8 | | vex 2740 |
. . . . . . . . . . . . 13
 |
9 | | vex 2740 |
. . . . . . . . . . . . 13
 |
10 | | vex 2740 |
. . . . . . . . . . . . 13
 |
11 | 8, 9, 10 | otth 4239 |
. . . . . . . . . . . 12
    
        |
12 | 7, 11 | sylibr 134 |
. . . . . . . . . . 11
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    
      |
13 | 12 | eqeq2d 2189 |
. . . . . . . . . 10
 
        
    |
14 | 13 | biimpd 144 |
. . . . . . . . 9
 
             |
15 | 14 | impancom 260 |
. . . . . . . 8
 
             |
16 | 15 | expimpd 363 |
. . . . . . 7
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<."   
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17 | 16 | exlimdv 1819 |
. . . . . 6
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    |
18 | 17 | exlimdvv 1897 |
. . . . 5
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    |
19 | | tru 1357 |
. . . . . . . . . . 11
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20 | 2 | adantr 276 |
. . . . . . . . . . . . 13
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21 | 3 | ad2antrr 488 |
. . . . . . . . . . . . . 14
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22 | | simpr 110 |
. . . . . . . . . . . . . . . . . . 19
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("    |
23 | 22, 11 | sylibr 134 |
. . . . . . . . . . . . . . . . . 18
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      |
24 | 23 | eqcomd 2183 |
. . . . . . . . . . . . . . . . 17
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>."  |
25 | 6 | biimpar 297 |
. . . . . . . . . . . . . . . . 17
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26 | 24, 25 | jca 306 |
. . . . . . . . . . . . . . . 16
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("    
       |
27 | | a1tru 1369 |
. . . . . . . . . . . . . . . 16
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   |
28 | 26, 27 | 2thd 175 |
. . . . . . . . . . . . . . 15
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("    
    
   |
29 | 28 | 3anassrs 1229 |
. . . . . . . . . . . . . 14
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("    
    
  |
30 | 21, 29 | sbcied 2999 |
. . . . . . . . . . . . 13
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    
  |
31 | 20, 30 | sbcied 2999 |
. . . . . . . . . . . 12
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  |
32 | 1, 31 | sbcied 2999 |
. . . . . . . . . . 11
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a" ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)    
    
   |
33 | 19, 32 | mpbiri 168 |
. . . . . . . . . 10
   ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)     
       |
34 | 33 | spesbcd 3049 |
. . . . . . . . 9
     ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)             |
35 | | nfcv 2319 |
. . . . . . . . . 10
   |
36 | | nfsbc1v 2981 |
. . . . . . . . . . 11
    ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)     
      |
37 | 36 | nfex 1637 |
. . . . . . . . . 10
      ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)            |
38 | | sbceq1a 2972 |
. . . . . . . . . . 11
  
 ![]. ].](_drbrack.gif)     
    
  ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)    
    
    |
39 | 38 | exbidv 1825 |
. . . . . . . . . 10
      ![]. ].](_drbrack.gif)    
    
     ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)    
    
    |
40 | 35, 37, 39 | spcegf 2820 |
. . . . . . . . 9
      ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)    
    
     
 ![]. ].](_drbrack.gif)     
        |
41 | 2, 34, 40 | sylc 62 |
. . . . . . . 8
     
 ![]. ].](_drbrack.gif)     
       |
42 | | nfcv 2319 |
. . . . . . . . 9
   |
43 | | nfsbc1v 2981 |
. . . . . . . . . . 11
    ![]. ].](_drbrack.gif)     
      |
44 | 43 | nfex 1637 |
. . . . . . . . . 10
      ![]. ].](_drbrack.gif)            |
45 | 44 | nfex 1637 |
. . . . . . . . 9
      
 ![]. ].](_drbrack.gif)     
      |
46 | | sbceq1a 2972 |
. . . . . . . . . 10
      
    
  ![]. ].](_drbrack.gif)    
    
    |
47 | 46 | 2exbidv 1868 |
. . . . . . . . 9
               
      ![]. ].](_drbrack.gif)    
    
    |
48 | 42, 45, 47 | spcegf 2820 |
. . . . . . . 8
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    
    |
49 | 3, 41, 48 | sylc 62 |
. . . . . . 7
          
    
   |
50 | | excom13 1689 |
. . . . . . 7
          
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)" |
51 | 49, 50 | sylib 122 |
. . . . . 6
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)" |
52 | | eqeq1 2184 |
. . . . . . . 8
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<."       |
53 | 52 | anbi1d 465 |
. . . . . . 7
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             |
54 | 53 | 3exbidv 1869 |
. . . . . 6
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         alt="<.
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          
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<."   
    |
55 | 51, 54 | syl5ibrcom 157 |
. . . . 5
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56 | 18, 55 | impbid 129 |
. . . 4
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57 | 56 | alrimiv 1874 |
. . 3
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58 | | eqeq2 2187 |
. . . . . 6
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59 | 58 | bibi2d 232 |
. . . . 5
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60 | 59 | albidv 1824 |
. . . 4
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("            
        |
61 | 60 | spcegv 2825 |
. . 3
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              alt="<.
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                      
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62 | 5, 57, 61 | sylc 62 |
. 2
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("            
   |
63 | | df-eu 2029 |
. 2
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64 | 62, 63 | sylibr 134 |
1
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