Proof of Theorem 4atexlemc
Step | Hyp | Ref
| Expression |
1 | | 4thatlem0.c |
. . 3
  
    |
2 | | 4thatlem.ph |
. . . . 5
     
    
 
    

     
      |
3 | 2 | 4atexlemkl 30539 |
. . . 4
   |
4 | | 4thatlem0.j |
. . . . 5
     |
5 | | 4thatlem0.a |
. . . . 5
     |
6 | 2, 4, 5 | 4atexlemqtb 30543 |
. . . 4
         |
7 | 2, 4, 5 | 4atexlempsb 30542 |
. . . 4
         |
8 | | eqid 2404 |
. . . . 5
         |
9 | | 4thatlem0.m |
. . . . 5
     |
10 | 8, 9 | latmcom 14459 |
. . . 4
  
    
      
   
          |
11 | 3, 6, 7, 10 | syl3anc 1184 |
. . 3
   
     
     |
12 | 1, 11 | syl5eq 2448 |
. 2
         |
13 | 2 | 4atexlemk 30529 |
. . 3
   |
14 | 2 | 4atexlemp 30532 |
. . 3
   |
15 | 2 | 4atexlems 30534 |
. . 3
   |
16 | 2 | 4atexlemq 30533 |
. . 3
   |
17 | 2 | 4atexlemt 30535 |
. . 3
   |
18 | | 4thatlem0.l |
. . . 4
     |
19 | 2, 18, 4, 5 | 4atexlempns 30544 |
. . 3
   |
20 | | 4thatlem0.h |
. . . . 5
     |
21 | | 4thatlem0.u |
. . . . 5
  
  |
22 | | 4thatlem0.v |
. . . . 5
  
  |
23 | 2, 18, 4, 9, 5, 20,
21, 22 | 4atexlemntlpq 30550 |
. . . 4
     |
24 | 18, 4, 5 | atnlej2 29862 |
. . . . 5
  

     |
25 | 24 | necomd 2650 |
. . . 4
  

     |
26 | 13, 17, 14, 16, 23, 25 | syl131anc 1197 |
. . 3
   |
27 | 2 | 4atexlempnq 30537 |
. . . 4
   |
28 | 2 | 4atexlemnslpq 30538 |
. . . 4
     |
29 | 18, 4, 5 | 4atlem0ae 30076 |
. . . 4
  

    
    |
30 | 13, 14, 16, 15, 27, 28, 29 | syl132anc 1202 |
. . 3
     |
31 | 8, 5 | atbase 29772 |
. . . . 5
       |
32 | 17, 31 | syl 16 |
. . . 4
       |
33 | 2, 18, 4, 9, 5, 20,
21 | 4atexlemu 30546 |
. . . . 5
   |
34 | 2, 18, 4, 9, 5, 20,
21, 22 | 4atexlemv 30547 |
. . . . 5
   |
35 | 8, 4, 5 | hlatjcl 29849 |
. . . . 5
 
         |
36 | 13, 33, 34, 35 | syl3anc 1184 |
. . . 4
         |
37 | 8, 5 | atbase 29772 |
. . . . . 6
       |
38 | 16, 37 | syl 16 |
. . . . 5
       |
39 | 8, 4 | latjcl 14434 |
. . . . 5
  
    
    
          |
40 | 3, 7, 38, 39 | syl3anc 1184 |
. . . 4
           |
41 | 2 | 4atexlemkc 30540 |
. . . . 5
   |
42 | 2, 18, 4, 9, 5, 20,
21, 22 | 4atexlemunv 30548 |
. . . . 5
   |
43 | 2 | 4atexlemutvt 30536 |
. . . . 5
       |
44 | 5, 18, 4 | cvlsupr4 29828 |
. . . . 5
  
       
    |
45 | 41, 33, 34, 17, 42, 43, 44 | syl132anc 1202 |
. . . 4

    |
46 | 8, 4, 5 | hlatjcl 29849 |
. . . . . . . . 9
 
         |
47 | 13, 14, 16, 46 | syl3anc 1184 |
. . . . . . . 8
         |
48 | 2, 20 | 4atexlemwb 30541 |
. . . . . . . 8
       |
49 | 8, 18, 9 | latmle1 14460 |
. . . . . . . 8
  
    
    
   
    |
50 | 3, 47, 48, 49 | syl3anc 1184 |
. . . . . . 7
   
     |
51 | 21, 50 | syl5eqbr 4205 |
. . . . . 6

    |
52 | 8, 18, 9 | latmle1 14460 |
. . . . . . . 8
  
    
    
   
    |
53 | 3, 7, 48, 52 | syl3anc 1184 |
. . . . . . 7
   
     |
54 | 22, 53 | syl5eqbr 4205 |
. . . . . 6

    |
55 | 8, 5 | atbase 29772 |
. . . . . . . 8
       |
56 | 33, 55 | syl 16 |
. . . . . . 7
       |
57 | 8, 5 | atbase 29772 |
. . . . . . . 8
       |
58 | 34, 57 | syl 16 |
. . . . . . 7
       |
59 | 8, 18, 4 | latjlej12 14451 |
. . . . . . 7
  
    
      
                    
   
     |
60 | 3, 56, 47, 58, 7, 59 | syl122anc 1193 |
. . . . . 6
         
   
     |
61 | 51, 54, 60 | mp2and 661 |
. . . . 5
      
    |
62 | 4, 5 | hlatjass 29852 |
. . . . . . 7
  
    
  
    |
63 | 13, 14, 16, 15, 62 | syl13anc 1186 |
. . . . . 6
      
    |
64 | 8, 5 | atbase 29772 |
. . . . . . . 8
       |
65 | 14, 64 | syl 16 |
. . . . . . 7
       |
66 | 8, 5 | atbase 29772 |
. . . . . . . 8
       |
67 | 15, 66 | syl 16 |
. . . . . . 7
       |
68 | 8, 4 | latj32 14481 |
. . . . . . 7
  
   
                    |
69 | 3, 65, 38, 67, 68 | syl13anc 1186 |
. . . . . 6
           |
70 | 8, 4 | latjjdi 14487 |
. . . . . . 7
  
   
                 
    |
71 | 3, 65, 38, 67, 70 | syl13anc 1186 |
. . . . . 6
        
    |
72 | 63, 69, 71 | 3eqtr3rd 2445 |
. . . . 5
             |
73 | 61, 72 | breqtrd 4196 |
. . . 4
         |
74 | 8, 18, 3, 32, 36, 40, 45, 73 | lattrd 14442 |
. . 3

      |
75 | 18, 4, 9, 5 | 2atmat 30043 |
. . 3
  
 

  
  
     
     |
76 | 13, 14, 15, 16, 17, 19, 26, 30, 74, 75 | syl333anc 1216 |
. 2
   
     |
77 | 12, 76 | eqeltrd 2478 |
1
   |