Step | Hyp | Ref
| Expression |
1 | | bren 6741 |
. . . . . . 7
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       |
2 | 1 | biimpi 120 |
. . . . . 6
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3 | 2 | ad2antrr 488 |
. . . . 5
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Markov
   
      |
4 | | f1ofn 5458 |
. . . . . . . . . . . 12
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  |
5 | 4 | ad3antlr 493 |
. . . . . . . . . . 11
     
Markov         
          |
6 | | f1ocnv 5470 |
. . . . . . . . . . . . . 14
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       |
7 | 6 | ad3antlr 493 |
. . . . . . . . . . . . 13
     
Markov         
               |
8 | | f1of 5457 |
. . . . . . . . . . . . 13
             |
9 | 7, 8 | syl 14 |
. . . . . . . . . . . 12
     
Markov         
               |
10 | | simpr 110 |
. . . . . . . . . . . 12
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Markov         
          |
11 | 9, 10 | ffvelcdmd 5648 |
. . . . . . . . . . 11
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Markov         
               |
12 | | fvco2 5581 |
. . . . . . . . . . 11
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("                          |
13 | 5, 11, 12 | syl2anc 411 |
. . . . . . . . . 10
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Markov    alt=")
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14 | | fveqeq2 5520 |
. . . . . . . . . . 11
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15 | | simplr 528 |
. . . . . . . . . . 11
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Markov         
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("       
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16 | 14, 15, 11 | rspcdva 2846 |
. . . . . . . . . 10
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Markov         
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("                    |
17 | | simpllr 534 |
. . . . . . . . . . . 12
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Markov         
              |
18 | | f1ocnvfv2 5773 |
. . . . . . . . . . . 12
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            |
19 | 17, 18 | sylancom 420 |
. . . . . . . . . . 11
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Markov         
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("                  |
20 | 19 | fveq2d 5515 |
. . . . . . . . . 10
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Markov         
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("                          |
21 | 13, 16, 20 | 3eqtr3rd 2219 |
. . . . . . . . 9
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Markov         
              |
22 | 21 | ralrimiva 2550 |
. . . . . . . 8
     Markov         
       
      |
23 | 22 | ex 115 |
. . . . . . 7
    Markov
       
 
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("    

       |
24 | 23 | con3d 631 |
. . . . . 6
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)"            |
26 | 25 | eqeq1d 2186 |
. . . . . . . . . 10
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("   
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27 | 26 | ralbidv 2477 |
. . . . . . . . 9
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         |
28 | 27 | notbid 667 |
. . . . . . . 8
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29 | 25 | eqeq1d 2186 |
. . . . . . . . 9
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("   
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30 | 29 | rexbidv 2478 |
. . . . . . . 8
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31 | 28, 30 | imbi12d 234 |
. . . . . . 7
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(" 
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)"  
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32 | | ismkvmap 7146 |
. . . . . . . . 9
 Markov  Markov                    |
33 | 32 | ibi 176 |
. . . . . . . 8
 Markov      
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34 | 33 | ad3antlr 493 |
. . . . . . 7
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       
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)"  
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f"  
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35 | | simpr 110 |
. . . . . . . . . . 11
  
Markov
       |
36 | | 2onn 6516 |
. . . . . . . . . . . . 13
 |
37 | | relen 6738 |
. . . . . . . . . . . . . 14
 |
38 | 37 | brrelex2i 4667 |
. . . . . . . . . . . . 13
   |
39 | | elmapg 6655 |
. . . . . . . . . . . . 13
 
           |
40 | 36, 38, 39 | sylancr 414 |
. . . . . . . . . . . 12
   
       |
41 | 40 | ad2antrr 488 |
. . . . . . . . . . 11
  
Markov
             |
42 | 35, 41 | mpbid 147 |
. . . . . . . . . 10
  
Markov
         |
43 | 42 | adantr 276 |
. . . . . . . . 9
    Markov
       
      |
44 | | f1of 5457 |
. . . . . . . . . 10
    
      |
45 | 44 | adantl 277 |
. . . . . . . . 9
    Markov
       
      |
46 | | fco 5377 |
. . . . . . . . 9
                   |
47 | 43, 45, 46 | syl2anc 411 |
. . . . . . . 8
    Markov
       
        |
48 | | simpllr 534 |
. . . . . . . . 9
    Markov
       
Markov |
49 | | elmapg 6655 |
. . . . . . . . 9
 
Markov     
         |
50 | 36, 48, 49 | sylancr 414 |
. . . . . . . 8
    Markov
       
    
         |
51 | 47, 50 | mpbird 167 |
. . . . . . 7
    Markov
       
      |
52 | 31, 34, 51 | rspcdva 2846 |
. . . . . 6
    Markov
       
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53 | 4 | ad2antlr 489 |
. . . . . . . . . 10
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)"         |
54 | | fvco2 5581 |
. . . . . . . . . 10
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55 | 53, 54 | sylancom 420 |
. . . . . . . . 9
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)"                    |
56 | 55 | eqeq1d 2186 |
. . . . . . . 8
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)"             
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)"    |
57 | 45 | ffvelcdmda 5647 |
. . . . . . . . 9
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)"             |
58 | | simpr 110 |
. . . . . . . . . 10
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Markov                     |
59 | 58 | fveqeq2d 5519 |
. . . . . . . . 9
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Markov                               |
60 | 57, 59 | rspcedv 2845 |
. . . . . . . 8
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)"               
       |
61 | 56, 60 | sylbid 150 |
. . . . . . 7
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)"              
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62 | 61 | rexlimdva 2594 |
. . . . . 6
    Markov
       
 
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("    

       |
63 | 24, 52, 62 | 3syld 57 |
. . . . 5
    Markov
       
      
       |
64 | 3, 63 | exlimddv 1898 |
. . . 4
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Markov
    
            |
65 | 64 | ralrimiva 2550 |
. . 3
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Markov                   |
66 | | ismkvmap 7146 |
. . . . 5
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Markov      
             |
67 | 38, 66 | syl 14 |
. . . 4
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Markov      
             |
68 | 67 | adantr 276 |
. . 3
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Markov  Markov
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             |
69 | 65, 68 | mpbird 167 |
. 2
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Markov Markov |
70 | 69 | ex 115 |
1
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Markov Markov  |