Step | Hyp | Ref
| Expression |
1 | | intex 4557 |
. . . 4
    |
2 | 1 | biimpi 199 |
. . 3

   |
3 | 2 | adantr 472 |
. 2
   sigAlgebra      |
4 | | intssuni 4248 |
. . . 4

    |
5 | 4 | adantr 472 |
. . 3
   sigAlgebra       |
6 | | simpr 468 |
. . . . 5
   sigAlgebra    sigAlgebra    |
7 | | elpwi 3951 |
. . . . . 6
  sigAlgebra 
sigAlgebra    |
8 | | sigasspw 29012 |
. . . . . . . 8
 sigAlgebra 
   |
9 | | selpw 3949 |
. . . . . . . 8
      |
10 | 8, 9 | sylibr 217 |
. . . . . . 7
 sigAlgebra      |
11 | 10 | ssriv 3422 |
. . . . . 6
sigAlgebra 
   |
12 | 7, 11 | syl6ss 3430 |
. . . . 5
  sigAlgebra 
    |
13 | 6, 12 | syl 17 |
. . . 4
   sigAlgebra       |
14 | | sspwuni 4360 |
. . . 4
  
    |
15 | 13, 14 | sylib 201 |
. . 3
   sigAlgebra       |
16 | 5, 15 | sstrd 3428 |
. 2
   sigAlgebra       |
17 | | simpr 468 |
. . . . . . . . 9
    sigAlgebra   
  |
18 | | simplr 770 |
. . . . . . . . 9
    sigAlgebra   
 sigAlgebra    |
19 | | elelpwi 3953 |
. . . . . . . . 9
 
 sigAlgebra   sigAlgebra    |
20 | 17, 18, 19 | syl2anc 673 |
. . . . . . . 8
    sigAlgebra   
sigAlgebra    |
21 | | vex 3034 |
. . . . . . . . 9
 |
22 | | issiga 29007 |
. . . . . . . . 9
  sigAlgebra   

   
         |
23 | 21, 22 | ax-mp 5 |
. . . . . . . 8
 sigAlgebra 
  
   
        |
24 | 20, 23 | sylib 201 |
. . . . . . 7
    sigAlgebra   
  
   
        |
25 | 24 | simprd 470 |
. . . . . 6
    sigAlgebra   


    
     |
26 | 25 | simp1d 1042 |
. . . . 5
    sigAlgebra   
  |
27 | 26 | ralrimiva 2809 |
. . . 4
   sigAlgebra   
  |
28 | | n0 3732 |
. . . . . . . . 9
    |
29 | 28 | biimpi 199 |
. . . . . . . 8

   |
30 | 29 | adantr 472 |
. . . . . . 7
   sigAlgebra      |
31 | 20 | ex 441 |
. . . . . . . 8
   sigAlgebra   
sigAlgebra     |
32 | 31 | eximdv 1772 |
. . . . . . 7
   sigAlgebra     
sigAlgebra     |
33 | 30, 32 | mpd 15 |
. . . . . 6
   sigAlgebra    sigAlgebra    |
34 | | elfvex 5906 |
. . . . . . 7
 sigAlgebra 
  |
35 | 34 | exlimiv 1784 |
. . . . . 6
  sigAlgebra    |
36 | 33, 35 | syl 17 |
. . . . 5
   sigAlgebra     |
37 | | elintg 4234 |
. . . . 5
 


   |
38 | 36, 37 | syl 17 |
. . . 4
   sigAlgebra    

   |
39 | 27, 38 | mpbird 240 |
. . 3
   sigAlgebra      |
40 | | simpll 768 |
. . . . . . . 8
     sigAlgebra        sigAlgebra     |
41 | | simpr 468 |
. . . . . . . 8
     sigAlgebra        |
42 | 40, 41 | jca 541 |
. . . . . . 7
     sigAlgebra         sigAlgebra      |
43 | | elinti 4235 |
. . . . . . . . 9
  
   |
44 | 43 | imp 436 |
. . . . . . . 8
  

  |
45 | 44 | adantll 728 |
. . . . . . 7
     sigAlgebra        |
46 | 25 | simp2d 1043 |
. . . . . . . 8
    sigAlgebra   

    |
47 | 46 | r19.21bi 2776 |
. . . . . . 7
     sigAlgebra   
     |
48 | 42, 45, 47 | syl2anc 673 |
. . . . . 6
     sigAlgebra          |
49 | 48 | ralrimiva 2809 |
. . . . 5
    sigAlgebra     
    |
50 | | difexg 4545 |
. . . . . . . 8
     |
51 | 36, 50 | syl 17 |
. . . . . . 7
   sigAlgebra       |
52 | 51 | adantr 472 |
. . . . . 6
    sigAlgebra         |
53 | | elintg 4234 |
. . . . . 6
             |
54 | 52, 53 | syl 17 |
. . . . 5
    sigAlgebra               |
55 | 49, 54 | mpbird 240 |
. . . 4
    sigAlgebra          |
56 | 55 | ralrimiva 2809 |
. . 3
   sigAlgebra           |
57 | | simplll 776 |
. . . . . . . . . 10
      sigAlgebra      
   sigAlgebra     |
58 | | simpr 468 |
. . . . . . . . . 10
      sigAlgebra      
   |
59 | 57, 58 | jca 541 |
. . . . . . . . 9
      sigAlgebra      
    sigAlgebra      |
60 | | simpllr 777 |
. . . . . . . . . 10
      sigAlgebra      
     |
61 | | elpwi 3951 |
. . . . . . . . . . . 12
  
   |
62 | | intss1 4241 |
. . . . . . . . . . . 12
    |
63 | 61, 62 | sylan9ss 3431 |
. . . . . . . . . . 11
    
  |
64 | | selpw 3949 |
. . . . . . . . . . 11
 
  |
65 | 63, 64 | sylibr 217 |
. . . . . . . . . 10
    
   |
66 | 60, 65 | sylancom 680 |
. . . . . . . . 9
      sigAlgebra      
    |
67 | 59, 66 | jca 541 |
. . . . . . . 8
      sigAlgebra      
     sigAlgebra   
    |
68 | | simplr 770 |
. . . . . . . 8
      sigAlgebra      
   |
69 | 25 | simp3d 1044 |
. . . . . . . . 9
    sigAlgebra   
  
    |
70 | 69 | r19.21bi 2776 |
. . . . . . . 8
     sigAlgebra   
  
    |
71 | 67, 68, 70 | sylc 61 |
. . . . . . 7
      sigAlgebra      
    |
72 | 71 | ralrimiva 2809 |
. . . . . 6
     sigAlgebra      

   |
73 | | uniexg 6607 |
. . . . . . . 8
      |
74 | 73 | ad2antlr 741 |
. . . . . . 7
     sigAlgebra      
   |
75 | | elintg 4234 |
. . . . . . 7
 
    
   |
76 | 74, 75 | syl 17 |
. . . . . 6
     sigAlgebra      
 


    |
77 | 72, 76 | mpbird 240 |
. . . . 5
     sigAlgebra      
    |
78 | 77 | ex 441 |
. . . 4
    sigAlgebra      
     |
79 | 78 | ralrimiva 2809 |
. . 3
   sigAlgebra            |
80 | 39, 56, 79 | 3jca 1210 |
. 2
   sigAlgebra     
     
         |
81 | | issiga 29007 |
. . 3
 
  sigAlgebra 
   
          
        |
82 | 81 | biimpar 493 |
. 2
     

                
 sigAlgebra    |
83 | 3, 16, 80, 82 | syl12anc 1290 |
1
   sigAlgebra    sigAlgebra    |