Step | Hyp | Ref
| Expression |
1 | | undifss 3515 |
. . . . . . . 8

      |
2 | 1 | biimpi 120 |
. . . . . . 7
       |
3 | 2 | adantl 277 |
. . . . . 6
 EXMID
  
 
  |
4 | | elun1 3314 |
. . . . . . . . . . 11
  
    |
5 | 4 | adantl 277 |
. . . . . . . . . 10
  EXMID    
    |
6 | | simplr 528 |
. . . . . . . . . . . 12
  EXMID     |
7 | | simpr 110 |
. . . . . . . . . . . 12
  EXMID  
  |
8 | 6, 7 | eldifd 3151 |
. . . . . . . . . . 11
  EXMID       |
9 | | elun2 3315 |
. . . . . . . . . . 11
    
    |
10 | 8, 9 | syl 14 |
. . . . . . . . . 10
  EXMID    
    |
11 | | exmidexmid 4208 |
. . . . . . . . . . . 12
EXMID
DECID
  |
12 | | exmiddc 837 |
. . . . . . . . . . . 12
DECID

   |
13 | 11, 12 | syl 14 |
. . . . . . . . . . 11
EXMID     |
14 | 13 | adantr 276 |
. . . . . . . . . 10
 EXMID      |
15 | 5, 10, 14 | mpjaodan 799 |
. . . . . . . . 9
 EXMID        |
16 | 15 | ex 115 |
. . . . . . . 8
EXMID         |
17 | 16 | ssrdv 3173 |
. . . . . . 7
EXMID  
    |
18 | 17 | adantr 276 |
. . . . . 6
 EXMID

      |
19 | 3, 18 | eqssd 3184 |
. . . . 5
 EXMID
  
    |
20 | 19 | ex 115 |
. . . 4
EXMID 
       |
21 | | ssun1 3310 |
. . . . 5


   |
22 | | sseq2 3191 |
. . . . 5
     
   
   |
23 | 21, 22 | mpbii 148 |
. . . 4
       |
24 | 20, 23 | impbid1 142 |
. . 3
EXMID 
       |
25 | 24 | alrimivv 1885 |
. 2
EXMID       
     |
26 | | vex 2752 |
. . . . . 6
 |
27 | | p0ex 4200 |
. . . . . 6
   |
28 | | sseq12 3192 |
. . . . . . . 8
 
   
     |
29 | | simpl 109 |
. . . . . . . . . 10
 
     |
30 | | simpr 110 |
. . . . . . . . . . 11
 
       |
31 | 30, 29 | difeq12d 3266 |
. . . . . . . . . 10
 
           |
32 | 29, 31 | uneq12d 3302 |
. . . . . . . . 9
 
          
    |
33 | 32, 30 | eqeq12d 2202 |
. . . . . . . 8
 
                   |
34 | 28, 33 | bibi12d 235 |
. . . . . . 7
 
    
       
            |
35 | 34 | spc2gv 2840 |
. . . . . 6
   
        
     
            |
36 | 26, 27, 35 | mp2an 426 |
. . . . 5
     
    
  
           |
37 | | 0ex 4142 |
. . . . . . . 8
 |
38 | 37 | snid 3635 |
. . . . . . 7
   |
39 | | eleq2 2251 |
. . . . . . 7
    
   
    
 
     |
40 | 38, 39 | mpbiri 168 |
. . . . . 6
    
   
   
    |
41 | | eldifn 3270 |
. . . . . . . 8
       |
42 | 41 | orim2i 762 |
. . . . . . 7
 
         |
43 | | elun 3288 |
. . . . . . 7
      
   
    |
44 | | df-dc 836 |
. . . . . . 7
DECID     |
45 | 42, 43, 44 | 3imtr4i 201 |
. . . . . 6
      
DECID   |
46 | 40, 45 | syl 14 |
. . . . 5
    
   
DECID   |
47 | 36, 46 | biimtrdi 163 |
. . . 4
     
    
  
DECID    |
48 | 47 | alrimiv 1884 |
. . 3
     
    
     DECID    |
49 | | df-exmid 4207 |
. . 3
EXMID
     DECID    |
50 | 48, 49 | sylibr 134 |
. 2
     
    
EXMID |
51 | 25, 50 | impbii 126 |
1
EXMID
      
     |