Proof of Theorem xrmaxiflemlub
Step | Hyp | Ref
| Expression |
1 | | xrmaxiflemlub.clt |
. . 3
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)"     |
2 | | xrmaxiflemlub.c |
. . . 4
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3 | | xrmaxiflemlub.a |
. . . . 5
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4 | | xrmaxiflemlub.b |
. . . . 5
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5 | | xrmaxiflemcl 11237 |
. . . . 5
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6 | 3, 4, 5 | syl2anc 411 |
. . . 4
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7 | | xrltso 9783 |
. . . . 5
 |
8 | | sowlin 4317 |
. . . . 5
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9 | 7, 8 | mpan 424 |
. . . 4
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10 | 2, 6, 3, 9 | syl3anc 1238 |
. . 3
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11 | 1, 10 | mpd 13 |
. 2
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)"      |
12 | 1 | adantr 276 |
. . . . 5
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               |
13 | 3 | adantr 276 |
. . . . . 6
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                    |
14 | 4 | adantr 276 |
. . . . . 6
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                    |
15 | | simplr 528 |
. . . . . . . . 9
                              
                              |
16 | | simpr 110 |
. . . . . . . . . 10
                              
   |
17 | 16 | iftrued 3541 |
. . . . . . . . 9
                              
                              |
18 | 15, 17 | breqtrd 4026 |
. . . . . . . 8
                              
   |
19 | 18, 16 | breqtrrd 4028 |
. . . . . . 7
                              
   |
20 | | simplr 528 |
. . . . . . . . . . . 12
                              
  
     
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                   |
21 | | simpr 110 |
. . . . . . . . . . . . 13
                              
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22 | 21 | iffalsed 3544 |
. . . . . . . . . . . 12
                              
                
                                   |
23 | 20, 22 | breqtrd 4026 |
. . . . . . . . . . 11
                              
  
                      |
24 | 23 | adantr 276 |
. . . . . . . . . 10
                   
                         
            |
25 | | simpr 110 |
. . . . . . . . . . 11
                   
                |
26 | 25 | iftrued 3541 |
. . . . . . . . . 10
                   
               
                      |
27 | 24, 26 | breqtrd 4026 |
. . . . . . . . 9
                   
                |
28 | | xrltnr 9766 |
. . . . . . . . . . 11

  |
29 | 3, 28 | syl 14 |
. . . . . . . . . 10
   |
30 | 29 | ad3antrrr 492 |
. . . . . . . . 9
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                |
31 | 27, 30 | pm2.21dd 620 |
. . . . . . . 8
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                |
32 | 23 | adantr 276 |
. . . . . . . . . . . . 13
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)"    
    
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                  |
33 | | simpr 110 |
. . . . . . . . . . . . . 14
                   
            
   |
34 | 33 | iffalsed 3544 |
. . . . . . . . . . . . 13
                   
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)"    
            
                             |
35 | 32, 34 | breqtrd 4026 |
. . . . . . . . . . . 12
                   
            
                    |
36 | 35 | adantr 276 |
. . . . . . . . . . 11
                                 

  
     
           |
37 | | simpr 110 |
. . . . . . . . . . . 12
                                 

   |
38 | 37 | iftrued 3541 |
. . . . . . . . . . 11
                                 

                    |
39 | 36, 38 | breqtrd 4026 |
. . . . . . . . . 10
                                 

   |
40 | | nltpnft 9801 |
. . . . . . . . . . . . 13


   |
41 | 3, 40 | syl 14 |
. . . . . . . . . . . 12
     |
42 | 41 | ad4antr 494 |
. . . . . . . . . . 11
                                 
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 
   |
43 | 37, 42 | mpbid 147 |
. . . . . . . . . 10
                                 


  |
44 | 39, 43 | pm2.21dd 620 |
. . . . . . . . 9
                                 
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   |
45 | 35 | adantr 276 |
. . . . . . . . . . . . 13
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)"    
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     
           |
46 | | simpr 110 |
. . . . . . . . . . . . . 14
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)"    
 
  |
47 | 46 | iffalsed 3544 |
. . . . . . . . . . . . 13
                                 
                                 |
48 | 45, 47 | breqtrd 4026 |
. . . . . . . . . . . 12
                                 
   
            |
49 | 48 | adantr 276 |
. . . . . . . . . . 11
     
       
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                 
                  |
50 | | simpr 110 |
. . . . . . . . . . . 12
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                 
      |
51 | 50 | iftrued 3541 |
. . . . . . . . . . 11
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                 
     
            |
52 | 49, 51 | breqtrd 4026 |
. . . . . . . . . 10
     
       
 
                 
      |
53 | 29 | ad5antr 496 |
. . . . . . . . . . 11
     
       
 
                 
  
   |
54 | | simp-5l 543 |
. . . . . . . . . . . . . . . . 17
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       
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55 | | simp-4r 542 |
. . . . . . . . . . . . . . . . 17
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                 
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56 | 54, 55 | jca 306 |
. . . . . . . . . . . . . . . 16
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)" |
57 | | simpllr 534 |
. . . . . . . . . . . . . . . 16
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                 
  
   |
58 | 56, 57 | jca 306 |
. . . . . . . . . . . . . . 15
     
       
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                 
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    |
59 | | simplr 528 |
. . . . . . . . . . . . . . 15
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                 
  
   |
60 | 58, 59 | jca 306 |
. . . . . . . . . . . . . 14
     
       
 
                 
  
     
   |
61 | | simpr 110 |
. . . . . . . . . . . . . 14
     
       
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                 
  
   |
62 | | simplr 528 |
. . . . . . . . . . . . . . 15
      
 
  |
63 | | simpr 110 |
. . . . . . . . . . . . . . 15
      
 
  |
64 | | elxr 9763 |
. . . . . . . . . . . . . . . . 17

    |
65 | 3, 64 | sylib 122 |
. . . . . . . . . . . . . . . 16
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   |
66 | 65 | ad4antr 494 |
. . . . . . . . . . . . . . 15
      
      |
67 | 62, 63, 66 | ecase23d 1350 |
. . . . . . . . . . . . . 14
      
    |
68 | 60, 61, 67 | syl2anc 411 |
. . . . . . . . . . . . 13
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       
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                 
  
   |
69 | | simp-4r 542 |
. . . . . . . . . . . . . . 15
      
 
  |
70 | | simpllr 534 |
. . . . . . . . . . . . . . 15
      
 
  |
71 | | elxr 9763 |
. . . . . . . . . . . . . . . . 17

    |
72 | 4, 71 | sylib 122 |
. . . . . . . . . . . . . . . 16
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   |
73 | 72 | ad4antr 494 |
. . . . . . . . . . . . . . 15
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      |
74 | 69, 70, 73 | ecase23d 1350 |
. . . . . . . . . . . . . 14
      
    |
75 | 60, 61, 74 | syl2anc 411 |
. . . . . . . . . . . . 13
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       
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                 
  
   |
76 | 48 | adantr 276 |
. . . . . . . . . . . . . 14
     
       
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                 
  
    
          |
77 | 61 | iffalsed 3544 |
. . . . . . . . . . . . . 14
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                 
  
                  
   |
78 | 76, 77 | breqtrd 4026 |
. . . . . . . . . . . . 13
     
       
 
                 
  
          |
79 | | maxleastlt 11208 |
. . . . . . . . . . . . 13
              
   |
80 | 68, 75, 68, 78, 79 | syl22anc 1239 |
. . . . . . . . . . . 12
     
       
 
                 
  
 
   |
81 | 80 | orcomd 729 |
. . . . . . . . . . 11
     
       
 
                 
  
 
   |
82 | 53, 81 | ecased 1349 |
. . . . . . . . . 10
     
       
 
                 
  
   |
83 | | xrmnfdc 9830 |
. . . . . . . . . . . 12

DECID
  |
84 | | exmiddc 836 |
. . . . . . . . . . . 12
DECID
    |
85 | 3, 83, 84 | 3syl 17 |
. . . . . . . . . . 11
     |
86 | 85 | ad4antr 494 |
. . . . . . . . . 10
                                 
      |
87 | 52, 82, 86 | mpjaodan 798 |
. . . . . . . . 9
                                 
    |
88 | | xrpnfdc 9829 |
. . . . . . . . . . 11

DECID
  |
89 | | exmiddc 836 |
. . . . . . . . . . 11
DECID
    |
90 | 3, 88, 89 | 3syl 17 |
. . . . . . . . . 10
     |
91 | 90 | ad3antrrr 492 |
. . . . . . . . 9
                   
            
     |
92 | 44, 87, 91 | mpjaodan 798 |
. . . . . . . 8
                   
            
   |
93 | | xrmnfdc 9830 |
. . . . . . . . . 10

DECID
  |
94 | | exmiddc 836 |
. . . . . . . . . 10
DECID
    |
95 | 4, 93, 94 | 3syl 17 |
. . . . . . . . 9
     |
96 | 95 | ad2antrr 488 |
. . . . . . . 8
                              
     |
97 | 31, 92, 96 | mpjaodan 798 |
. . . . . . 7
                              
   |
98 | | xrpnfdc 9829 |
. . . . . . . 8

DECID
  |
99 | | exmiddc 836 |
. . . . . . . 8
DECID
    |
100 | 14, 98, 99 | 3syl 17 |
. . . . . . 7
 
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   |
101 | 19, 97, 100 | mpjaodan 798 |
. . . . . 6
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                    |
102 | 13, 14, 101 | xrmaxiflemab 11239 |
. . . . 5
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     
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                   |
103 | 12, 102 | breqtrd 4026 |
. . . 4
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       
 
                    |
104 | 103 | ex 115 |
. . 3
   
     
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                
   |
105 | 104 | orim2d 788 |
. 2
                               
    |
106 | 11, 105 | mpd 13 |
1
 
   |