Step | Hyp | Ref
| Expression |
1 | | ltsonq 7388 |
. . . . . 6
 |
2 | | ltrelnq 7355 |
. . . . . 6
   |
3 | 1, 2 | son2lpi 5021 |
. . . . 5
   |
4 | | ltrelpr 7495 |
. . . . . . . . . . . . . . . 16
   |
5 | 4 | brel 4675 |
. . . . . . . . . . . . . . 15

    |
6 | 5 | simprd 114 |
. . . . . . . . . . . . . 14

  |
7 | | prop 7465 |
. . . . . . . . . . . . . 14
              |
8 | 6, 7 | syl 14 |
. . . . . . . . . . . . 13

             |
9 | | prltlu 7477 |
. . . . . . . . . . . . 13
                                |
10 | 8, 9 | syl3an1 1271 |
. . . . . . . . . . . 12
 
                   |
11 | 10 | 3expb 1204 |
. . . . . . . . . . 11
 
                     |
12 | 11 | adantlr 477 |
. . . . . . . . . 10
  
                      |
13 | 12 | adantrll 484 |
. . . . . . . . 9
  
      
                     |
14 | 13 | adantrrl 486 |
. . . . . . . 8
  
      
           
               |
15 | | ltanqg 7390 |
. . . . . . . . . 10
 
 
       |
16 | 15 | adantl 277 |
. . . . . . . . 9
          
           
         
 
        |
17 | 5 | simpld 112 |
. . . . . . . . . . . . 13

  |
18 | | prop 7465 |
. . . . . . . . . . . . 13
              |
19 | 17, 18 | syl 14 |
. . . . . . . . . . . 12

             |
20 | | elprnqu 7472 |
. . . . . . . . . . . 12
                    |
21 | 19, 20 | sylan 283 |
. . . . . . . . . . 11
 
       |
22 | 21 | ad2ant2r 509 |
. . . . . . . . . 10
  
                |
23 | 22 | adantrr 479 |
. . . . . . . . 9
  
      
           
           |
24 | | elprnql 7471 |
. . . . . . . . . . . 12
                    |
25 | 19, 24 | sylan 283 |
. . . . . . . . . . 11
 
       |
26 | 25 | ad2ant2r 509 |
. . . . . . . . . 10
  
                |
27 | 26 | adantrl 478 |
. . . . . . . . 9
  
      
           
           |
28 | | simplr 528 |
. . . . . . . . 9
  
      
           
           |
29 | | addcomnqg 7371 |
. . . . . . . . . 10
 
       |
30 | 29 | adantl 277 |
. . . . . . . . 9
          
           
           
      |
31 | 16, 23, 27, 28, 30 | caovord2d 6038 |
. . . . . . . 8
  
      
           
                 |
32 | 14, 31 | mpbird 167 |
. . . . . . 7
  
      
           
           |
33 | | prltlu 7477 |
. . . . . . . . . . . . 13
                        |
34 | 19, 33 | syl3an1 1271 |
. . . . . . . . . . . 12
 
           |
35 | 34 | 3com23 1209 |
. . . . . . . . . . 11
 
           |
36 | 35 | 3expb 1204 |
. . . . . . . . . 10
 
             |
37 | 36 | adantlr 477 |
. . . . . . . . 9
  
              |
38 | 37 | adantrlr 485 |
. . . . . . . 8
  
      
               |
39 | 38 | adantrrr 487 |
. . . . . . 7
  
      
           
           |
40 | 32, 39 | jca 306 |
. . . . . 6
  
      
           
         
   |
41 | 40 | ex 115 |
. . . . 5
 
       
           
             |
42 | 3, 41 | mtoi 664 |
. . . 4
 
      
           
          |
43 | 42 | alrimivv 1875 |
. . 3
 
         
           
          |
44 | | ltexprlem.1 |
. . . . . . . . . . . 12
        
                
          |
45 | 44 | ltexprlemell 7588 |
. . . . . . . . . . 11
     
                 |
46 | 44 | ltexprlemelu 7589 |
. . . . . . . . . . 11
     
                 |
47 | 45, 46 | anbi12i 460 |
. . . . . . . . . 10
          
        
               
           |
48 | | anandi 590 |
. . . . . . . . . 10
         
                      
        
               
           |
49 | 47, 48 | bitr4i 187 |
. . . . . . . . 9
          
        
                         |
50 | 49 | baib 919 |
. . . . . . . 8
                                             |
51 | | eleq1 2240 |
. . . . . . . . . . 11
     
       |
52 | | oveq1 5876 |
. . . . . . . . . . . 12
       |
53 | 52 | eleq1d 2246 |
. . . . . . . . . . 11
       
         |
54 | 51, 53 | anbi12d 473 |
. . . . . . . . . 10
                  
          |
55 | 54 | cbvexv 1918 |
. . . . . . . . 9
       
             
         |
56 | 55 | anbi2i 457 |
. . . . . . . 8
        
                     
       
                        |
57 | 50, 56 | bitrdi 196 |
. . . . . . 7
                                             |
58 | | eeanv 1932 |
. . . . . . 7
                      
       
       
                        |
59 | 57, 58 | bitr4di 198 |
. . . . . 6
                     
           
           |
60 | 59 | notbid 667 |
. . . . 5
           
         
           
           |
61 | | alnex 1499 |
. . . . . . 7
       
           
       
       
           
          |
62 | 61 | albii 1470 |
. . . . . 6
                     
       
                               |
63 | | alnex 1499 |
. . . . . 6
                     
       
         
           
          |
64 | 62, 63 | bitri 184 |
. . . . 5
                     
       
         
           
          |
65 | 60, 64 | bitr4di 198 |
. . . 4
                    
           
           |
66 | 65 | adantl 277 |
. . 3
 
      
             
           
           |
67 | 43, 66 | mpbird 167 |
. 2
 
     
       |
68 | 67 | ralrimiva 2550 |
1

     
       |