Step | Hyp | Ref
| Expression |
1 | | df-cross 5765 |
. . 3
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2 | | rexcom 2773 |
. . . . 5
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3 | | elxp2 4803 |
. . . . 5
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4 | | elin 3220 |
. . . . . . . 8
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S Ins4 SI3 Ins2        1c     
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Ins2 S          
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S Ins4 SI3 Ins2        1c   |
5 | | snex 4112 |
. . . . . . . . . . 11
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6 | 5 | otelins2 5792 |
. . . . . . . . . 10
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S         Ins2
S  |
7 | | vex 2863 |
. . . . . . . . . . 11
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8 | 7 | otelins2 5792 |
. . . . . . . . . 10
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S    
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9 | | vex 2863 |
. . . . . . . . . . 11
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10 | | vex 2863 |
. . . . . . . . . . 11
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11 | 9, 10 | opelssetsn 4761 |
. . . . . . . . . 10
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12 | 6, 8, 11 | 3bitri 262 |
. . . . . . . . 9
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S
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13 | 10 | oqelins4 5795 |
. . . . . . . . . 10
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S Ins4 SI3 Ins2        1c            Ins2 Ins2
S Ins4 SI3 Ins2        1c  |
14 | | elin 3220 |
. . . . . . . . . . . . 13
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SI3 Ins2                       Ins2 Ins2 S    
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15 | | snex 4112 |
. . . . . . . . . . . . . . . 16
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16 | 15 | otelins2 5792 |
. . . . . . . . . . . . . . 15
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17 | 5 | otelins2 5792 |
. . . . . . . . . . . . . . 15
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18 | | vex 2863 |
. . . . . . . . . . . . . . . 16
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19 | 18, 7 | opelssetsn 4761 |
. . . . . . . . . . . . . . 15
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20 | 16, 17, 19 | 3bitri 262 |
. . . . . . . . . . . . . 14
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21 | 7 | oqelins4 5795 |
. . . . . . . . . . . . . . 15
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Ins2                  SI3 Ins2        |
22 | | vex 2863 |
. . . . . . . . . . . . . . . 16
 |
23 | 18, 9, 22 | otsnelsi3 5806 |
. . . . . . . . . . . . . . 15
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24 | | elin 3220 |
. . . . . . . . . . . . . . . 16
  
    Ins2        
    Ins2              |
25 | 9 | otelins2 5792 |
. . . . . . . . . . . . . . . . . 18
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26 | | df-br 4641 |
. . . . . . . . . . . . . . . . . 18
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27 | | brcnv 4893 |
. . . . . . . . . . . . . . . . . 18
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28 | 25, 26, 27 | 3bitr2i 264 |
. . . . . . . . . . . . . . . . 17
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29 | | opelxp 4812 |
. . . . . . . . . . . . . . . . . . 19
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30 | 18, 29 | mpbiran 884 |
. . . . . . . . . . . . . . . . . 18
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31 | | df-br 4641 |
. . . . . . . . . . . . . . . . . 18
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32 | | brcnv 4893 |
. . . . . . . . . . . . . . . . . 18
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33 | 30, 31, 32 | 3bitr2i 264 |
. . . . . . . . . . . . . . . . 17
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34 | 28, 33 | anbi12i 678 |
. . . . . . . . . . . . . . . 16
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35 | 18, 9 | op1st2nd 5791 |
. . . . . . . . . . . . . . . 16
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36 | 24, 34, 35 | 3bitri 262 |
. . . . . . . . . . . . . . 15
  
    Ins2           |
37 | 21, 23, 36 | 3bitri 262 |
. . . . . . . . . . . . . 14
                Ins4 SI3
Ins2           |
38 | 20, 37 | anbi12i 678 |
. . . . . . . . . . . . 13
                 Ins2
Ins2 S                Ins4 SI3
Ins2      

      |
39 | 14, 38 | bitri 240 |
. . . . . . . . . . . 12
                Ins2 Ins2 S Ins4
SI3 Ins2              |
40 | 39 | exbii 1582 |
. . . . . . . . . . 11
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SI3 Ins2         
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41 | | elima1c 4948 |
. . . . . . . . . . 11
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SI3 Ins2        1c      
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   Ins2 Ins2 S Ins4 SI3 Ins2         |
42 | | df-rex 2621 |
. . . . . . . . . . 11
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43 | 40, 41, 42 | 3bitr4i 268 |
. . . . . . . . . 10
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SI3 Ins2        1c 
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44 | 13, 43 | bitri 240 |
. . . . . . . . 9
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45 | 12, 44 | anbi12i 678 |
. . . . . . . 8
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S              Ins4  Ins2 Ins2 S Ins4 SI3 Ins2        1c  
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46 | 4, 45 | bitri 240 |
. . . . . . 7
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S Ins4 SI3 Ins2        1c  
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47 | 46 | exbii 1582 |
. . . . . 6
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48 | | elima1c 4948 |
. . . . . 6
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49 | | df-rex 2621 |
. . . . . 6
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50 | 47, 48, 49 | 3bitr4i 268 |
. . . . 5
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51 | 2, 3, 50 | 3bitr4ri 269 |
. . . 4
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   Ins2 Ins2 S Ins4  Ins2 Ins2
S Ins4 SI3 Ins2        1c  1c     |
52 | 51 | releqmpt2 5810 |
. . 3
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Ins2 S Ins3  Ins2 Ins2 S Ins4  Ins2 Ins2
S Ins4 SI3 Ins2        1c  1c  1c  
    |
53 | 1, 52 | eqtr4i 2376 |
. 2
Cross       Ins2 S
Ins3  Ins2 Ins2 S Ins4  Ins2 Ins2
S Ins4 SI3 Ins2        1c  1c  1c  |
54 | | vvex 4110 |
. . 3
 |
55 | | ssetex 4745 |
. . . . . . 7
S  |
56 | 55 | ins2ex 5798 |
. . . . . 6
Ins2 S  |
57 | 56 | ins2ex 5798 |
. . . . 5
Ins2 Ins2 S  |
58 | | 1stex 4740 |
. . . . . . . . . . . . 13
 |
59 | 58 | cnvex 5103 |
. . . . . . . . . . . 12
  |
60 | 59 | ins2ex 5798 |
. . . . . . . . . . 11
Ins2   |
61 | | 2ndex 5113 |
. . . . . . . . . . . . 13
 |
62 | 61 | cnvex 5103 |
. . . . . . . . . . . 12
  |
63 | 54, 62 | xpex 5116 |
. . . . . . . . . . 11
    |
64 | 60, 63 | inex 4106 |
. . . . . . . . . 10
Ins2     
 |
65 | 64 | si3ex 5807 |
. . . . . . . . 9
SI3 Ins2       |
66 | 65 | ins4ex 5800 |
. . . . . . . 8
Ins4 SI3
Ins2     
 |
67 | 57, 66 | inex 4106 |
. . . . . . 7
Ins2 Ins2 S Ins4 SI3 Ins2        |
68 | | 1cex 4143 |
. . . . . . 7
1c
 |
69 | 67, 68 | imaex 4748 |
. . . . . 6
 Ins2 Ins2 S Ins4
SI3 Ins2        1c  |
70 | 69 | ins4ex 5800 |
. . . . 5
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71 | 57, 70 | inex 4106 |
. . . 4
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72 | 71, 68 | imaex 4748 |
. . 3
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73 | 54, 54, 72 | mpt2exlem 5812 |
. 2
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74 | 53, 73 | eqeltri 2423 |
1
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