Step | Hyp | Ref
| Expression |
1 | | euotd.1 |
. . . 4
   |
2 | | euotd.2 |
. . . 4
   |
3 | | euotd.3 |
. . . 4
   |
4 | | otexg 3958 |
. . . 4
 
       |
5 | 1, 2, 3, 4 | syl3anc 1134 |
. . 3
    
  |
6 | | euotd.4 |
. . . . . . . . . . . . 13
  
    |
7 | 6 | biimpa 280 |
. . . . . . . . . . . 12
   
   |
8 | | vex 2554 |
. . . . . . . . . . . . 13
 |
9 | | vex 2554 |
. . . . . . . . . . . . 13
 |
10 | | vex 2554 |
. . . . . . . . . . . . 13
 |
11 | 8, 9, 10 | otth 3970 |
. . . . . . . . . . . 12
    
  
 
   |
12 | 7, 11 | sylibr 137 |
. . . . . . . . . . 11
      
      |
13 | 12 | eqeq2d 2048 |
. . . . . . . . . 10
   
      
    |
14 | 13 | biimpd 132 |
. . . . . . . . 9
   
           |
15 | 14 | impancom 247 |
. . . . . . . 8
      
        |
16 | 15 | expimpd 345 |
. . . . . . 7
      
   
    |
17 | 16 | exlimdv 1697 |
. . . . . 6
         
  
    |
18 | 17 | exlimdvv 1774 |
. . . . 5
             
  
    |
19 | | tru 1246 |
. . . . . . . . . . 11
 |
20 | 2 | adantr 261 |
. . . . . . . . . . . . 13
     |
21 | 3 | ad2antrr 457 |
. . . . . . . . . . . . . 14
       |
22 | | simpr 103 |
. . . . . . . . . . . . . . . . . . 19
     
   |
23 | 22, 11 | sylibr 137 |
. . . . . . . . . . . . . . . . . 18
        
      |
24 | 23 | eqcomd 2042 |
. . . . . . . . . . . . . . . . 17
               |
25 | 6 | biimpar 281 |
. . . . . . . . . . . . . . . . 17
       |
26 | 24, 25 | jca 290 |
. . . . . . . . . . . . . . . 16
         
       |
27 | | a1tru 1258 |
. . . . . . . . . . . . . . . 16
      |
28 | 26, 27 | 2thd 164 |
. . . . . . . . . . . . . . 15
          
       |
29 | 28 | 3anassrs 1125 |
. . . . . . . . . . . . . 14
   

               |
30 | 21, 29 | sbcied 2793 |
. . . . . . . . . . . . 13
      
 ![]. ].](_drbrack.gif)     
       |
31 | 20, 30 | sbcied 2793 |
. . . . . . . . . . . 12
      ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)             |
32 | 1, 31 | sbcied 2793 |
. . . . . . . . . . 11
    ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)    
    
   |
33 | 19, 32 | mpbiri 157 |
. . . . . . . . . 10
   ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)     
       |
34 | 33 | spesbcd 2838 |
. . . . . . . . 9
     ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)             |
35 | | nfcv 2175 |
. . . . . . . . . 10
   |
36 | | nfsbc1v 2776 |
. . . . . . . . . . 11
    ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)     
      |
37 | 36 | nfex 1525 |
. . . . . . . . . 10
      ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)            |
38 | | sbceq1a 2767 |
. . . . . . . . . . 11
  
 ![]. ].](_drbrack.gif)     
       ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)              |
39 | 38 | exbidv 1703 |
. . . . . . . . . 10
      ![]. ].](_drbrack.gif)    
    
     ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)    
    
    |
40 | 35, 37, 39 | spcegf 2630 |
. . . . . . . . 9
      ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)    
    
     
 ![]. ].](_drbrack.gif)     
        |
41 | 2, 34, 40 | sylc 56 |
. . . . . . . 8
     
 ![]. ].](_drbrack.gif)     
       |
42 | | nfcv 2175 |
. . . . . . . . 9
   |
43 | | nfsbc1v 2776 |
. . . . . . . . . . 11
    ![]. ].](_drbrack.gif)     
      |
44 | 43 | nfex 1525 |
. . . . . . . . . 10
      ![]. ].](_drbrack.gif)            |
45 | 44 | nfex 1525 |
. . . . . . . . 9
      
 ![]. ].](_drbrack.gif)     
      |
46 | | sbceq1a 2767 |
. . . . . . . . . 10
      
       ![]. ].](_drbrack.gif)              |
47 | 46 | 2exbidv 1745 |
. . . . . . . . 9
                      ![]. ].](_drbrack.gif)    
    
    |
48 | 42, 45, 47 | spcegf 2630 |
. . . . . . . 8
        ![]. ].](_drbrack.gif)                    
    
    |
49 | 3, 41, 48 | sylc 56 |
. . . . . . 7
          
    
   |
50 | | excom13 1576 |
. . . . . . 7
           
                       |
51 | 49, 50 | sylib 127 |
. . . . . 6
          
    
   |
52 | | eqeq1 2043 |
. . . . . . . 8
    

               |
53 | 52 | anbi1d 438 |
. . . . . . 7
    
 
                  |
54 | 53 | 3exbidv 1746 |
. . . . . 6
    
           
          
    
    |
55 | 51, 54 | syl5ibrcom 146 |
. . . . 5
                     |
56 | 18, 55 | impbid 120 |
. . . 4
                     |
57 | 56 | alrimiv 1751 |
. . 3
          
            |
58 | | eqeq2 2046 |
. . . . . 6
    

       |
59 | 58 | bibi2d 221 |
. . . . 5
    
            

            

  
     |
60 | 59 | albidv 1702 |
. . . 4
    
                              

  
     |
61 | 60 | spcegv 2635 |
. . 3
                                     
         |
62 | 5, 57, 61 | sylc 56 |
. 2
                

   |
63 | | df-eu 1900 |
. 2
                                   |
64 | 62, 63 | sylibr 137 |
1
                 |