Step | Hyp | Ref
| Expression |
1 | | prop 7465 |
. . . . . . 7
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)"   |
2 | | prnmaxl 7478 |
. . . . . . 7
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)"           
       |
3 | 1, 2 | sylan 283 |
. . . . . 6
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       |
4 | 3 | ad2ant2rl 511 |
. . . . 5
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)"   |
5 | | ltexnqi 7399 |
. . . . . . 7
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6 | 5 | ad2antll 491 |
. . . . . 6
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7 | | simplr 528 |
. . . . . . . . 9
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8 | 7 | ad2antrr 488 |
. . . . . . . 8
      
          
   
  
  |
9 | | simprl 529 |
. . . . . . . 8
      
          
   
  
  |
10 | | prop 7465 |
. . . . . . . . 9
              |
11 | | prarloc2 7494 |
. . . . . . . . 9
                            |
12 | 10, 11 | sylan 283 |
. . . . . . . 8
 
               |
13 | 8, 9, 12 | syl2anc 411 |
. . . . . . 7
      
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)"         |
14 | 8 | adantr 276 |
. . . . . . . . . 10
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                        
          |
15 | | simprl 529 |
. . . . . . . . . 10
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                        
              |
16 | | elprnql 7471 |
. . . . . . . . . . 11
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)"          
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17 | 10, 16 | sylan 283 |
. . . . . . . . . 10
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18 | 14, 15, 17 | syl2anc 411 |
. . . . . . . . 9
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          |
19 | | simpll 527 |
. . . . . . . . . . 11
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20 | 19 | ad3antrrr 492 |
. . . . . . . . . 10
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          |
21 | | simprr 531 |
. . . . . . . . . . 11
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)"  |
22 | 21 | ad3antrrr 492 |
. . . . . . . . . 10
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)"  |
23 | | elprnql 7471 |
. . . . . . . . . . 11
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)"          
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24 | 1, 23 | sylan 283 |
. . . . . . . . . 10
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25 | 20, 22, 24 | syl2anc 411 |
. . . . . . . . 9
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26 | | nqtri3or 7386 |
. . . . . . . . 9
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27 | 18, 25, 26 | syl2anc 411 |
. . . . . . . 8
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        
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28 | 18 | adantr 276 |
. . . . . . . . . . . . . 14
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           |
29 | | simplrl 535 |
. . . . . . . . . . . . . . 15
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          |
30 | 29 | adantr 276 |
. . . . . . . . . . . . . 14
                               
           |
31 | | addclnq 7365 |
. . . . . . . . . . . . . 14
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32 | 28, 30, 31 | syl2anc 411 |
. . . . . . . . . . . . 13
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             |
33 | | ltanqg 7390 |
. . . . . . . . . . . . . . . . . 18
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       |
34 | 33 | adantl 277 |
. . . . . . . . . . . . . . . . 17
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        
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("        |
35 | | addcomnqg 7371 |
. . . . . . . . . . . . . . . . . 18
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       |
36 | 35 | adantl 277 |
. . . . . . . . . . . . . . . . 17
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        
 
      |
37 | 34, 18, 25, 29, 36 | caovord2d 6038 |
. . . . . . . . . . . . . . . 16
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                        
        
       |
38 | | simplrr 536 |
. . . . . . . . . . . . . . . . . 18
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            |
39 | | simprl 529 |
. . . . . . . . . . . . . . . . . . 19
   

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          
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)"  |
40 | 39 | ad2antrr 488 |
. . . . . . . . . . . . . . . . . 18
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                        
              |
41 | 38, 40 | eqeltrd 2254 |
. . . . . . . . . . . . . . . . 17
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)"  |
42 | | prcdnql 7474 |
. . . . . . . . . . . . . . . . . 18
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43 | 1, 42 | sylan 283 |
. . . . . . . . . . . . . . . . 17
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("              |
44 | 20, 41, 43 | syl2anc 411 |
. . . . . . . . . . . . . . . 16
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                        
                      |
45 | 37, 44 | sylbid 150 |
. . . . . . . . . . . . . . 15
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                        
                  |
46 | | simprr 531 |
. . . . . . . . . . . . . . 15
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                        
                |
47 | 45, 46 | jctild 316 |
. . . . . . . . . . . . . 14
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                        
                          |
48 | 47 | imp 124 |
. . . . . . . . . . . . 13
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                         |
49 | | eleq1 2240 |
. . . . . . . . . . . . . . 15
       
         |
50 | | eleq1 2240 |
. . . . . . . . . . . . . . 15
       
         |
51 | 49, 50 | anbi12d 473 |
. . . . . . . . . . . . . 14
                    
          |
52 | 51 | rspcev 2841 |
. . . . . . . . . . . . 13
                        
       |
53 | 32, 48, 52 | syl2anc 411 |
. . . . . . . . . . . 12
                               
              
       |
54 | | ltdfpr 7496 |
. . . . . . . . . . . . . 14
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 
     
        |
55 | 14, 20, 54 | syl2anc 411 |
. . . . . . . . . . . . 13
     
                        
        
     
        |
56 | 55 | adantr 276 |
. . . . . . . . . . . 12
                               
         
     
        |
57 | 53, 56 | mpbird 167 |
. . . . . . . . . . 11
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           |
58 | | simplrl 535 |
. . . . . . . . . . . 12
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59 | 58 | ad3antrrr 492 |
. . . . . . . . . . 11
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60 | 57, 59 | pm2.21dd 620 |
. . . . . . . . . 10
                               
               |
61 | 60 | ex 115 |
. . . . . . . . 9
     
                        
                |
62 | | eleq1 2240 |
. . . . . . . . . 10
     
       |
63 | 15, 62 | syl5ibcom 155 |
. . . . . . . . 9
     
                        
        
       |
64 | | prcdnql 7474 |
. . . . . . . . . . 11
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<."                        |
65 | 10, 64 | sylan 283 |
. . . . . . . . . 10
 
             |
66 | 14, 15, 65 | syl2anc 411 |
. . . . . . . . 9
     
                        
                |
67 | 61, 63, 66 | 3jaod 1304 |
. . . . . . . 8
     
                        
         
        |
68 | 27, 67 | mpd 13 |
. . . . . . 7
     
                        
              |
69 | 13, 68 | rexlimddv 2599 |
. . . . . 6
      
          
   
  
      |
70 | 6, 69 | rexlimddv 2599 |
. . . . 5
   


          
        |
71 | 4, 70 | rexlimddv 2599 |
. . . 4
                 |
72 | 71 | expr 375 |
. . 3
         
       |
73 | 72 | 3impa 1194 |
. 2
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("            |
74 | 73 | ssrdv 3161 |
1
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("   
      |