Step | Hyp | Ref
| Expression |
1 | | euotd.1 |
. . . 4
   |
2 | | euotd.2 |
. . . 4
   |
3 | | euotd.3 |
. . . 4
   |
4 | | otexg 4230 |
. . . 4
 
   
   |
5 | 1, 2, 3, 4 | syl3anc 1238 |
. . 3
       |
6 | | euotd.4 |
. . . . . . . . . . . . 13
 

    |
7 | 6 | biimpa 296 |
. . . . . . . . . . . 12
 
     |
8 | | vex 2740 |
. . . . . . . . . . . . 13
 |
9 | | vex 2740 |
. . . . . . . . . . . . 13
 |
10 | | vex 2740 |
. . . . . . . . . . . . 13
 |
11 | 8, 9, 10 | otth 4242 |
. . . . . . . . . . . 12
    
        |
12 | 7, 11 | sylibr 134 |
. . . . . . . . . . 11
 
    
      |
13 | 12 | eqeq2d 2189 |
. . . . . . . . . 10
 
        
    |
14 | 13 | biimpd 144 |
. . . . . . . . 9
 
             |
15 | 14 | impancom 260 |
. . . . . . . 8
 
             |
16 | 15 | expimpd 363 |
. . . . . . 7
      
   
    |
17 | 16 | exlimdv 1819 |
. . . . . 6
         
  
    |
18 | 17 | exlimdvv 1897 |
. . . . 5
             
  
    |
19 | | tru 1357 |
. . . . . . . . . . 11
 |
20 | 2 | adantr 276 |
. . . . . . . . . . . . 13
 
   |
21 | 3 | ad2antrr 488 |
. . . . . . . . . . . . . 14
       |
22 | | simpr 110 |
. . . . . . . . . . . . . . . . . . 19
 

      |
23 | 22, 11 | sylibr 134 |
. . . . . . . . . . . . . . . . . 18
 

     
      |
24 | 23 | eqcomd 2183 |
. . . . . . . . . . . . . . . . 17
 

            |
25 | 6 | biimpar 297 |
. . . . . . . . . . . . . . . . 17
 

    |
26 | 24, 25 | jca 306 |
. . . . . . . . . . . . . . . 16
 

      
       |
27 | | a1tru 1369 |
. . . . . . . . . . . . . . . 16
 

   |
28 | 26, 27 | 2thd 175 |
. . . . . . . . . . . . . . 15
 

      
    
   |
29 | 28 | 3anassrs 1229 |
. . . . . . . . . . . . . 14
   


      
    
  |
30 | 21, 29 | sbcied 2999 |
. . . . . . . . . . . . 13
      
 ![]. ].](_drbrack.gif)     
    
  |
31 | 20, 30 | sbcied 2999 |
. . . . . . . . . . . 12
 
  
 ![]. ].](_drbrack.gif)   ![]. ].](_drbrack.gif)     
    
  |
32 | 1, 31 | sbcied 2999 |
. . . . . . . . . . 11
    ![]. ].](_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
        ![]. ].](_drbrack.gif)                    
    
    |
49 | 3, 41, 48 | sylc 62 |
. . . . . . 7
          
    
   |
50 | | excom13 1689 |
. . . . . . 7
          
    
          
    
   |
51 | 49, 50 | sylib 122 |
. . . . . 6
          
    
   |
52 | | eqeq1 2184 |
. . . . . . . 8
    
    
  
        |
53 | 52 | anbi1d 465 |
. . . . . . 7
    
      
             |
54 | 53 | 3exbidv 1869 |
. . . . . 6
    
           
          
    
    |
55 | 51, 54 | syl5ibrcom 157 |
. . . . 5
                
    |
56 | 18, 55 | impbid 129 |
. . . 4
             
       |
57 | 56 | alrimiv 1874 |
. . 3
              
        |
58 | | eqeq2 2187 |
. . . . . 6
    

       |
59 | 58 | bibi2d 232 |
. . . . 5
    
            
 
            
        |
60 | 59 | albidv 1824 |
. . . 4
    
               

              
        |
61 | 60 | spcegv 2825 |
. . 3
  
                
                      
    |
62 | 5, 57, 61 | sylc 62 |
. 2
                 
   |
63 | | df-eu 2029 |
. 2
              
                
   |
64 | 62, 63 | sylibr 134 |
1
                 |