Step | Hyp | Ref
| Expression |
1 | | prml 7467 |
. . . . . . 7
  
 
  |
2 | | df-rex 2461 |
. . . . . . 7
 
      |
3 | 1, 2 | sylib 122 |
. . . . . 6
  
       |
4 | 3 | adantr 276 |
. . . . 5
    

      |
5 | | prmu 7468 |
. . . . . . 7
  
 
  |
6 | | df-rex 2461 |
. . . . . . 7
 
      |
7 | 5, 6 | sylib 122 |
. . . . . 6
  
       |
8 | 7 | adantr 276 |
. . . . 5
    

      |
9 | | subhalfnqq 7404 |
. . . . . . . . 9
      |
10 | 9 | adantl 277 |
. . . . . . . 8
    

     |
11 | | df-rex 2461 |
. . . . . . . 8
   
        |
12 | 10, 11 | sylib 122 |
. . . . . . 7
    

        |
13 | 12 | ancli 323 |
. . . . . 6
    

    

         |
14 | | 19.42v 1906 |
. . . . . 6
      


         
          |
15 | 13, 14 | sylibr 134 |
. . . . 5
    

      
        |
16 | | eeeanv 1933 |
. . . . 5
          
     
              
       

        |
17 | 4, 8, 15, 16 | syl3anbrc 1181 |
. . . 4
    

         
               |
18 | | prarloclemarch2 7409 |
. . . . . . . . . . . . . 14
 
               |
19 | | df-rex 2461 |
. . . . . . . . . . . . . 14
            
   
             |
20 | 18, 19 | sylib 122 |
. . . . . . . . . . . . 13
 
    
             |
21 | 20 | 3com12 1207 |
. . . . . . . . . . . 12
 
    
             |
22 | 21 | 3adant1r 1231 |
. . . . . . . . . . 11
                      |
23 | 22 | 3adant2r 1233 |
. . . . . . . . . 10
    
     
             |
24 | 23 | 3adant3r 1235 |
. . . . . . . . 9
    
                       |
25 | 24 | 3adant3l 1234 |
. . . . . . . 8
    
            
   
             |
26 | 25 | ancli 323 |
. . . . . . 7
    
            
    
                
              |
27 | | 19.42v 1906 |
. . . . . . 7
     
      


                      
      


         
              |
28 | 26, 27 | sylibr 134 |
. . . . . 6
    
            
      
     
                       |
29 | 28 | 2eximi 1601 |
. . . . 5
        
            
        
 
     
                       |
30 | 29 | eximi 1600 |
. . . 4
          
     
      
          
      


                      |
31 | | simpl1l 1048 |
. . . . . . . . . 10
   
 
     
                    
  |
32 | | simp3rl 1070 |
. . . . . . . . . . 11
    
            
  |
33 | 32 | adantr 276 |
. . . . . . . . . 10
   
 
     
                    
  |
34 | | simp3rr 1071 |
. . . . . . . . . . 11
    
            
    |
35 | 34 | adantr 276 |
. . . . . . . . . 10
   
 
     
                    
    |
36 | 31, 33, 35 | 3jca 1177 |
. . . . . . . . 9
   
 
     
                    

     |
37 | | simp3ll 1068 |
. . . . . . . . . . . 12
    
            
     |
38 | 37 | adantr 276 |
. . . . . . . . . . 11
   
 
     
                    
     |
39 | | simpl1r 1049 |
. . . . . . . . . . 11
   
 
     
                    
  |
40 | | simprl 529 |
. . . . . . . . . . 11
   
 
     
                    
  |
41 | | simprrl 539 |
. . . . . . . . . . 11
   
 
     
                    
  |
42 | | simprrr 540 |
. . . . . . . . . . . 12
   
 
     
                    
           |
43 | | simpl2r 1051 |
. . . . . . . . . . . . 13
   
 
     
                    
  |
44 | | prcunqu 7475 |
. . . . . . . . . . . . 13
    
                       |
45 | 38, 43, 44 | syl2anc 411 |
. . . . . . . . . . . 12
   
 
     
                    
                      |
46 | 42, 45 | mpd 13 |
. . . . . . . . . . 11
   
 
     
                    
           |
47 | | prarloclem 7491 |
. . . . . . . . . . 11
       
             
+Q0      
~Q0 ·Q0   
             |
48 | 38, 39, 40, 33, 41, 46, 47 | syl231anc 1258 |
. . . . . . . . . 10
   
 
     
                    
   +Q0       ~Q0 ·Q0
  
             |
49 | | df-rex 2461 |
. . . . . . . . . 10
   
+Q0      
~Q0 ·Q0   
             
  +Q0       ~Q0 ·Q0
  
              |
50 | 48, 49 | sylib 122 |
. . . . . . . . 9
   
 
     
                    
    
+Q0      
~Q0 ·Q0   
              |
51 | 36, 50 | jca 306 |
. . . . . . . 8
   
 
     
                    
 
     
  +Q0       ~Q0 ·Q0
  
               |
52 | | 19.42v 1906 |
. . . . . . . 8
          
+Q0      
~Q0 ·Q0   
            
 
     
  +Q0       ~Q0 ·Q0
  
               |
53 | 51, 52 | sylibr 134 |
. . . . . . 7
   
 
     
                    
   
   
  +Q0       ~Q0 ·Q0
  
               |
54 | | simprrl 539 |
. . . . . . . . . . . 12
      
 
+Q0      
~Q0 ·Q0   
              +Q0       ~Q0 ·Q0
    |
55 | | eleq1 2240 |
. . . . . . . . . . . . . . . . 17
 
+Q0      
~Q0 ·Q0  


+Q0      
~Q0 ·Q0      |
56 | 55 | anbi1d 465 |
. . . . . . . . . . . . . . . 16
 
+Q0      
~Q0 ·Q0  
  
            
+Q0      
~Q0 ·Q0   
              |
57 | 56 | anbi2d 464 |
. . . . . . . . . . . . . . 15
 
+Q0      
~Q0 ·Q0  
                
  +Q0       ~Q0 ·Q0
  
               |
58 | 57 | anbi2d 464 |
. . . . . . . . . . . . . 14
 
+Q0      
~Q0 ·Q0  
      
              
 
     
+Q0      
~Q0 ·Q0   
                |
59 | 58 | ceqsexgv 2866 |
. . . . . . . . . . . . 13
  +Q0       ~Q0 ·Q0
       +Q0       ~Q0 ·Q0
 
 
                   
 
     
+Q0      
~Q0 ·Q0   
                |
60 | 59 | biimprcd 160 |
. . . . . . . . . . . 12
      
 
+Q0      
~Q0 ·Q0   
              
+Q0      
~Q0 ·Q0      
+Q0      
~Q0 ·Q0    
                       |
61 | 54, 60 | mpd 13 |
. . . . . . . . . . 11
      
 
+Q0      
~Q0 ·Q0   
                 +Q0       ~Q0 ·Q0
 
 
                      |
62 | | simprrr 540 |
. . . . . . . . . . 11
      
 
+Q0      
~Q0 ·Q0   
                   
      |
63 | | eleq1 2240 |
. . . . . . . . . . . . . . . . . 18
           

              |
64 | 63 | anbi2d 464 |
. . . . . . . . . . . . . . . . 17
           
 
  
              |
65 | 64 | anbi2d 464 |
. . . . . . . . . . . . . . . 16
           
  
 
        
         |
66 | 65 | anbi2d 464 |
. . . . . . . . . . . . . . 15
           
      

  
 
                      |
67 | 66 | anbi2d 464 |
. . . . . . . . . . . . . 14
           
   +Q0       ~Q0 ·Q0
 
 
    
      +Q0       ~Q0 ·Q0
 
 
                       |
68 | 67 | exbidv 1825 |
. . . . . . . . . . . . 13
           
    
+Q0      
~Q0 ·Q0    
    
       
+Q0      
~Q0 ·Q0    
                       |
69 | 68 | ceqsexgv 2866 |
. . . . . . . . . . . 12
       
   
                   +Q0       ~Q0 ·Q0
 
 
    
        
+Q0      
~Q0 ·Q0    
                       |
70 | 69 | biimprcd 160 |
. . . . . . . . . . 11
    
+Q0      
~Q0 ·Q0    
                                                  +Q0       ~Q0 ·Q0
 
 
    
        |
71 | 61, 62, 70 | sylc 62 |
. . . . . . . . . 10
      
 
+Q0      
~Q0 ·Q0   
                      
       
+Q0      
~Q0 ·Q0    
    
       |
72 | | 19.42v 1906 |
. . . . . . . . . . 11
                
+Q0      
~Q0 ·Q0    
    
                     +Q0       ~Q0 ·Q0
 
 
    
       |
73 | 72 | exbii 1605 |
. . . . . . . . . 10
                   +Q0       ~Q0 ·Q0
 
 
    
                       +Q0       ~Q0 ·Q0
 
 
    
       |
74 | 71, 73 | sylibr 134 |
. . . . . . . . 9
      
 
+Q0      
~Q0 ·Q0   
                              
+Q0      
~Q0 ·Q0    
    
       |
75 | | simprrl 539 |
. . . . . . . . . . . . . 14
      

     |
76 | 75 | adantl 277 |
. . . . . . . . . . . . 13
    +Q0       ~Q0 ·Q0
 

                

      |
77 | | simprrr 540 |
. . . . . . . . . . . . . . 15
      

     |
78 | 77 | adantl 277 |
. . . . . . . . . . . . . 14
    +Q0       ~Q0 ·Q0
 

                

      |
79 | | simpl 109 |
. . . . . . . . . . . . . . 15
    +Q0       ~Q0 ·Q0
 

                

     
+Q0      
~Q0 ·Q0                 |
80 | | simprl2 1043 |
. . . . . . . . . . . . . . . 16
    +Q0       ~Q0 ·Q0
 

                

      |
81 | | simprl3 1044 |
. . . . . . . . . . . . . . . 16
    +Q0       ~Q0 ·Q0
 

                

        |
82 | 80, 81 | jca 306 |
. . . . . . . . . . . . . . 15
    +Q0       ~Q0 ·Q0
 

                

    
     |
83 | | simprl1 1042 |
. . . . . . . . . . . . . . . 16
    +Q0       ~Q0 ·Q0
 

                

      |
84 | | simprrl 539 |
. . . . . . . . . . . . . . . 16
    +Q0       ~Q0 ·Q0
 

                

      |
85 | 83, 84 | jca 306 |
. . . . . . . . . . . . . . 15
    +Q0       ~Q0 ·Q0
 

                

    
   |
86 | | prarloclemcalc 7492 |
. . . . . . . . . . . . . . 15
    +Q0       ~Q0 ·Q0
 

                
       |
87 | 79, 82, 85, 86 | syl12anc 1236 |
. . . . . . . . . . . . . 14
    +Q0       ~Q0 ·Q0
 

                

        |
88 | 78, 87 | jca 306 |
. . . . . . . . . . . . 13
    +Q0       ~Q0 ·Q0
 

                

          |
89 | 76, 88 | jca 306 |
. . . . . . . . . . . 12
    +Q0       ~Q0 ·Q0
 

                

            |
90 | 89 | ancom1s 569 |
. . . . . . . . . . 11
         
   
 +Q0       ~Q0
·Q0          
            |
91 | 90 | anasss 399 |
. . . . . . . . . 10
               +Q0       ~Q0 ·Q0
 
 
    
    

       |
92 | 91 | 2eximi 1601 |
. . . . . . . . 9
                   +Q0       ~Q0 ·Q0
 
 
    
    
            |
93 | 74, 92 | syl 14 |
. . . . . . . 8
      
 
+Q0      
~Q0 ·Q0   
                         |
94 | 93 | exlimiv 1598 |
. . . . . . 7
          
+Q0      
~Q0 ·Q0   
                         |
95 | 53, 94 | syl 14 |
. . . . . 6
   
 
     
                    
            |
96 | 95 | exlimivv 1896 |
. . . . 5
       
 
     
                    
            |
97 | 96 | exlimivv 1896 |
. . . 4
           
 
     
                    
            |
98 | 17, 30, 97 | 3syl 17 |
. . 3
    

            |
99 | | excom 1664 |
. . 3
      
         
      |
100 | 98, 99 | sylib 122 |
. 2
    

            |
101 | | 19.42v 1906 |
. . . . 5
        

  
      |
102 | | df-rex 2461 |
. . . . . 6
            |
103 | 102 | anbi2i 457 |
. . . . 5
     

  
      |
104 | 101, 103 | bitr4i 187 |
. . . 4
        


     |
105 | 104 | exbii 1605 |
. . 3
      
       
     |
106 | | df-rex 2461 |
. . 3
  
     
     |
107 | 105, 106 | bitr4i 187 |
. 2
      
     
    |
108 | 100, 107 | sylib 122 |
1
    



    |