Step | Hyp | Ref
| Expression |
1 | | elpri 3614 |
. . . . . . . . . 10
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)"  |
2 | | exmidonfinlem.a |
. . . . . . . . . 10
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3 | 1, 2 | eleq2s 2272 |
. . . . . . . . 9
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4 | | eleq2 2241 |
. . . . . . . . . . . 12
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5 | 4 | biimpcd 159 |
. . . . . . . . . . 11
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6 | | elrabi 2890 |
. . . . . . . . . . . . . 14
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7 | | velsn 3608 |
. . . . . . . . . . . . . 14
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8 | 6, 7 | sylib 122 |
. . . . . . . . . . . . 13
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{"     |
9 | | biidd 172 |
. . . . . . . . . . . . . . . . . 18
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10 | 9 | elrab 2893 |
. . . . . . . . . . . . . . . . 17
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11 | 10 | simprbi 275 |
. . . . . . . . . . . . . . . 16
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12 | 11 | notnotd 630 |
. . . . . . . . . . . . . . 15
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  |
13 | | 0ex 4127 |
. . . . . . . . . . . . . . . . 17
 |
14 | 13 | snm 3711 |
. . . . . . . . . . . . . . . 16

   |
15 | | r19.3rmv 3513 |
. . . . . . . . . . . . . . . 16
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       |
16 | 14, 15 | ax-mp 5 |
. . . . . . . . . . . . . . 15
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17 | 12, 16 | sylib 122 |
. . . . . . . . . . . . . 14
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{"        |
18 | | rabeq0 3452 |
. . . . . . . . . . . . . 14
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19 | 17, 18 | sylibr 134 |
. . . . . . . . . . . . 13
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{"     |
20 | 8, 19 | eqtr4d 2213 |
. . . . . . . . . . . 12
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{"         |
21 | | p0ex 4185 |
. . . . . . . . . . . . . . 15
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22 | 21 | rabex 4144 |
. . . . . . . . . . . . . 14
     |
23 | 22 | prid2 3698 |
. . . . . . . . . . . . 13
          
     |
24 | 23, 2 | eleqtrri 2253 |
. . . . . . . . . . . 12
     |
25 | 20, 24 | eqeltrdi 2268 |
. . . . . . . . . . 11
       |
26 | 5, 25 | syl6 33 |
. . . . . . . . . 10
         |
27 | | eleq2 2241 |
. . . . . . . . . . . 12
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28 | 27 | biimpcd 159 |
. . . . . . . . . . 11
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29 | | elrabi 2890 |
. . . . . . . . . . . . . 14
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30 | 29, 7 | sylib 122 |
. . . . . . . . . . . . 13
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31 | | biidd 172 |
. . . . . . . . . . . . . . . . 17
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32 | 31 | elrab 2893 |
. . . . . . . . . . . . . . . 16
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33 | 32 | simprbi 275 |
. . . . . . . . . . . . . . 15
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34 | | r19.3rmv 3513 |
. . . . . . . . . . . . . . . 16
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35 | 14, 34 | ax-mp 5 |
. . . . . . . . . . . . . . 15
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36 | 33, 35 | sylib 122 |
. . . . . . . . . . . . . 14
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37 | | rabeq0 3452 |
. . . . . . . . . . . . . 14
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38 | 36, 37 | sylibr 134 |
. . . . . . . . . . . . 13
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39 | 30, 38 | eqtr4d 2213 |
. . . . . . . . . . . 12
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{"  
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     |
40 | 21 | rabex 4144 |
. . . . . . . . . . . . . 14
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41 | 40 | prid1 3697 |
. . . . . . . . . . . . 13
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42 | 41, 2 | eleqtrri 2253 |
. . . . . . . . . . . 12
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43 | 39, 42 | eqeltrdi 2268 |
. . . . . . . . . . 11
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44 | 28, 43 | syl6 33 |
. . . . . . . . . 10
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45 | 26, 44 | jaod 717 |
. . . . . . . . 9
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46 | 3, 45 | mpan9 281 |
. . . . . . . 8
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47 | 46 | rgen2 2563 |
. . . . . . 7
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48 | | dftr5 4101 |
. . . . . . 7
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49 | 47, 48 | mpbir 146 |
. . . . . 6
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50 | | elpri 3614 |
. . . . . . . . 9
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)"  |
51 | 50, 2 | eleq2s 2272 |
. . . . . . . 8
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)"  |
52 | | ordtriexmidlem 4515 |
. . . . . . . . . . 11
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53 | 52 | ontrci 4424 |
. . . . . . . . . 10
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54 | | treq 4104 |
. . . . . . . . . 10
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)"  |
55 | 53, 54 | mpbiri 168 |
. . . . . . . . 9
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{"  
  |
56 | | ordtriexmidlem 4515 |
. . . . . . . . . . 11
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57 | 56 | ontrci 4424 |
. . . . . . . . . 10
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58 | | treq 4104 |
. . . . . . . . . 10
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{"  
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{"      |
59 | 57, 58 | mpbiri 168 |
. . . . . . . . 9
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{"  
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)" |
60 | 55, 59 | jaoi 716 |
. . . . . . . 8
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   
  |
61 | 51, 60 | syl 14 |
. . . . . . 7
   |
62 | 61 | rgen 2530 |
. . . . . 6
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 |
63 | | dford3 4364 |
. . . . . 6
      |
64 | 49, 62, 63 | mpbir2an 942 |
. . . . 5
 |
65 | | prexg 4208 |
. . . . . . . 8
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{"   
       |
66 | 40, 22, 65 | mp2an 426 |
. . . . . . 7
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   
 |
67 | 2, 66 | eqeltri 2250 |
. . . . . 6
 |
68 | 67 | elon 4371 |
. . . . 5

  |
69 | 64, 68 | mpbir 146 |
. . . 4
 |
70 | | 2onn 6516 |
. . . . . 6
 |
71 | | nnfi 6866 |
. . . . . 6
   |
72 | 70, 71 | ax-mp 5 |
. . . . 5
 |
73 | | pm5.19 706 |
. . . . . . . . . 10
   |
74 | 13 | snm 3711 |
. . . . . . . . . . 11
    |
75 | | r19.3rmv 3513 |
. . . . . . . . . . 11
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ph"    |
76 | 74, 75 | ax-mp 5 |
. . . . . . . . . 10
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       |
77 | 73, 76 | mtbi 670 |
. . . . . . . . 9
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     |
78 | | rabbi 2654 |
. . . . . . . . 9
 
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      |
79 | 77, 78 | mtbi 670 |
. . . . . . . 8
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    |
80 | 79 | neir 2350 |
. . . . . . 7
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{"    |
81 | | pr2ne 7185 |
. . . . . . . 8
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)"  |
82 | 40, 22, 81 | mp2an 426 |
. . . . . . 7
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{"     |
83 | 80, 82 | mpbir 146 |
. . . . . 6
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84 | 2, 83 | eqbrtri 4021 |
. . . . 5
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85 | | enfii 6868 |
. . . . 5
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86 | 72, 84, 85 | mp2an 426 |
. . . 4
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87 | 69, 86 | elini 3319 |
. . 3
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88 | | eleq2 2241 |
. . 3
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89 | 87, 88 | mpbiri 168 |
. 2
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90 | | df1o2 6424 |
. . . . 5
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91 | | 1lt2o 6437 |
. . . . 5
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92 | 90, 91 | eqeltrri 2251 |
. . . 4
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93 | | nneneq 6851 |
. . . . . 6
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94 | 70, 93 | mpan2 425 |
. . . . 5
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95 | 84, 94 | mpbii 148 |
. . . 4
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96 | 92, 95 | eleqtrrid 2267 |
. . 3
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97 | | elpri 3614 |
. . . 4
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98 | 97, 2 | eleq2s 2272 |
. . 3
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99 | 96, 98 | syl 14 |
. 2
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       |
100 | 13 | snid 3622 |
. . . . . . 7
   |
101 | | eleq2 2241 |
. . . . . . 7
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(/)"
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       |
102 | 100, 101 | mpbii 148 |
. . . . . 6
  
          |
103 | | biidd 172 |
. . . . . . 7

    |
104 | 103 | elrab 2893 |
. . . . . 6
     
     |
105 | 102, 104 | sylib 122 |
. . . . 5
  
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     |
106 | 105 | simprd 114 |
. . . 4
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(/)"
      |
107 | | eleq2 2241 |
. . . . . . 7
  
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         |
108 | 100, 107 | mpbii 148 |
. . . . . 6
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(/)"
   
      |
109 | | biidd 172 |
. . . . . . 7

    |
110 | 109 | elrab 2893 |
. . . . . 6
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111 | 108, 110 | sylib 122 |
. . . . 5
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112 | 111 | simprd 114 |
. . . 4
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113 | 106, 112 | orim12i 759 |
. . 3
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114 | | df-dc 835 |
. . 3
DECID
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115 | 113, 114 | sylibr 134 |
. 2
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DECID   |
116 | 89, 99, 115 | 3syl 17 |
1
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