Step | Hyp | Ref
| Expression |
1 | | vex 2740 |
. . . . . . . . . 10
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_V" |
2 | | vex 2740 |
. . . . . . . . . 10
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3 | | eleq1 2240 |
. . . . . . . . . . . 12
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4 | 3 | anbi1d 465 |
. . . . . . . . . . 11
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5 | | eqeq1 2184 |
. . . . . . . . . . . . . 14
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6 | 5 | anbi1d 465 |
. . . . . . . . . . . . 13
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7 | 6 | anbi1d 465 |
. . . . . . . . . . . 12
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8 | 7 | 4exbidv 1870 |
. . . . . . . . . . 11
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9 | 4, 8 | anbi12d 473 |
. . . . . . . . . 10
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10 | | eleq1 2240 |
. . . . . . . . . . . 12
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11 | 10 | anbi2d 464 |
. . . . . . . . . . 11
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12 | | eqeq1 2184 |
. . . . . . . . . . . . . 14
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13 | 12 | anbi2d 464 |
. . . . . . . . . . . . 13
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14 | 13 | anbi1d 465 |
. . . . . . . . . . . 12
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)"    |
15 | 14 | 4exbidv 1870 |
. . . . . . . . . . 11
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16 | 11, 15 | anbi12d 473 |
. . . . . . . . . 10
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17 | | df-enq0 7414 |
. . . . . . . . . 10
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18 | 1, 2, 9, 16, 17 | brab 4269 |
. . . . . . . . 9
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19 | | vex 2740 |
. . . . . . . . . 10
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20 | | eleq1 2240 |
. . . . . . . . . . . 12
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21 | 20 | anbi1d 465 |
. . . . . . . . . . 11
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22 | | eqeq1 2184 |
. . . . . . . . . . . . . 14
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23 | 22 | anbi1d 465 |
. . . . . . . . . . . . 13
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24 | 23 | anbi1d 465 |
. . . . . . . . . . . 12
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25 | 24 | 4exbidv 1870 |
. . . . . . . . . . 11
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26 | 21, 25 | anbi12d 473 |
. . . . . . . . . 10
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27 | | eleq1 2240 |
. . . . . . . . . . . 12
   
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)"  |
28 | 27 | anbi2d 464 |
. . . . . . . . . . 11
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29 | | eqeq1 2184 |
. . . . . . . . . . . . . 14
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30 | 29 | anbi2d 464 |
. . . . . . . . . . . . 13
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31 | 30 | anbi1d 465 |
. . . . . . . . . . . 12
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32 | 31 | 4exbidv 1870 |
. . . . . . . . . . 11
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33 | 28, 32 | anbi12d 473 |
. . . . . . . . . 10
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34 | | df-enq0 7414 |
. . . . . . . . . 10
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35 | 2, 19, 26, 33, 34 | brab 4269 |
. . . . . . . . 9
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36 | 18, 35 | anbi12i 460 |
. . . . . . . 8
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37 | 36 | biimpi 120 |
. . . . . . 7
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39 | 37, 38 | sylib 122 |
. . . . . 6
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40 | | 3anass 982 |
. . . . . . . 8
                     |
41 | | anass 401 |
. . . . . . . . 9
    
         
                |
42 | | anass 401 |
. . . . . . . . . 10
    
                  |
43 | 42 | anbi2i 457 |
. . . . . . . . 9
       
      
                |
44 | | anidm 396 |
. . . . . . . . . . 11
      
    |
45 | 44 | anbi1i 458 |
. . . . . . . . . 10
    
              |
46 | 45 | anbi2i 457 |
. . . . . . . . 9
       
      
            |
47 | 41, 43, 46 | 3bitr2i 208 |
. . . . . . . 8
    
         
            |
48 | 40, 47 | bitr4i 187 |
. . . . . . 7
            
            |
49 | 48 | anbi1i 458 |
. . . . . 6
    
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50 | 39, 49 | sylibr 134 |
. . . . 5
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51 | | ee8anv 1935 |
. . . . . 6
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52 | 51 | anbi2i 457 |
. . . . 5
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53 | 50, 52 | sylibr 134 |
. . . 4
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54 | | 19.42vvvv 1913 |
. . . . . . 7
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55 | 54 | 2exbii 1606 |
. . . . . 6
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56 | 55 | 2exbii 1606 |
. . . . 5
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58 | 56, 57 | bitri 184 |
. . . 4
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60 | | 3simpb 995 |
. . . . . . . . 9
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61 | 60 | adantr 276 |
. . . . . . . 8
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62 | | simplll 533 |
. . . . . . . . . 10
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63 | | simprlr 538 |
. . . . . . . . . 10
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64 | 62, 63 | jca 306 |
. . . . . . . . 9
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65 | 64 | adantl 277 |
. . . . . . . 8
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68 | | simpl3 1002 |
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69 | 67, 68 | eqeltrrd 2255 |
. . . . . . . . . . . . . . . . . . . . 21
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)" |
70 | | opelxp 4653 |
. . . . . . . . . . . . . . . . . . . . 21
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s"        |
71 | 69, 70 | sylib 122 |
. . . . . . . . . . . . . . . . . . . 20
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)" |
72 | 71 | simprd 114 |
. . . . . . . . . . . . . . . . . . 19
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73 | | pinn 7299 |
. . . . . . . . . . . . . . . . . . 19
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74 | 72, 73 | syl 14 |
. . . . . . . . . . . . . . . . . 18
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75 | | nnm0r 6474 |
. . . . . . . . . . . . . . . . . 18
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76 | 74, 75 | syl 14 |
. . . . . . . . . . . . . . . . 17
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77 | 76 | eqeq2d 2189 |
. . . . . . . . . . . . . . . 16
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78 | 66, 77 | imbitrid 154 |
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79 | | simprr 531 |
. . . . . . . . . . . . . . . . . 18
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80 | | eqtr2 2196 |
. . . . . . . . . . . . . . . . . . . . . 22
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81 | | vex 2740 |
. . . . . . . . . . . . . . . . . . . . . . 23
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_V" |
82 | | vex 2740 |
. . . . . . . . . . . . . . . . . . . . . . 23
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_V" |
83 | 81, 82 | opth 4234 |
. . . . . . . . . . . . . . . . . . . . . 22
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)" |
84 | 80, 83 | sylib 122 |
. . . . . . . . . . . . . . . . . . . . 21
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>."
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85 | | oveq1 5876 |
. . . . . . . . . . . . . . . . . . . . . 22
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86 | | oveq1 5876 |
. . . . . . . . . . . . . . . . . . . . . 22
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87 | 85, 86 | eqeqan12d 2193 |
. . . . . . . . . . . . . . . . . . . . 21
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("       |
88 | 84, 87 | syl 14 |
. . . . . . . . . . . . . . . . . . . 20
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   
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       |
89 | 88 | ad2ant2lr 510 |
. . . . . . . . . . . . . . . . . . 19
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90 | 89 | ad2ant2r 509 |
. . . . . . . . . . . . . . . . . 18
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91 | 79, 90 | mpbird 167 |
. . . . . . . . . . . . . . . . 17
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92 | 91 | eqeq1d 2186 |
. . . . . . . . . . . . . . . 16
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93 | 92 | adantl 277 |
. . . . . . . . . . . . . . 15
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94 | 78, 93 | sylibd 149 |
. . . . . . . . . . . . . 14
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95 | | simpllr 534 |
. . . . . . . . . . . . . . . . . . . 20
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96 | 95 | adantl 277 |
. . . . . . . . . . . . . . . . . . 19
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97 | | simpl2 1001 |
. . . . . . . . . . . . . . . . . . 19
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98 | 96, 97 | eqeltrrd 2255 |
. . . . . . . . . . . . . . . . . 18
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99 | | opelxp 4653 |
. . . . . . . . . . . . . . . . . 18
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v"        |
100 | 98, 99 | sylib 122 |
. . . . . . . . . . . . . . . . 17
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)" |
101 | 100 | simprd 114 |
. . . . . . . . . . . . . . . 16
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102 | | pinn 7299 |
. . . . . . . . . . . . . . . 16
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103 | 101, 102 | syl 14 |
. . . . . . . . . . . . . . 15
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104 | 71 | simpld 112 |
. . . . . . . . . . . . . . 15
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105 | | nnm00 6525 |
. . . . . . . . . . . . . . 15
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106 | 103, 104,
105 | syl2anc 411 |
. . . . . . . . . . . . . 14
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107 | 94, 106 | sylibd 149 |
. . . . . . . . . . . . 13
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108 | | elni2 7304 |
. . . . . . . . . . . . . . . 16
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)"  |
109 | 108 | simprbi 275 |
. . . . . . . . . . . . . . 15
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)" |
110 | 101, 109 | syl 14 |
. . . . . . . . . . . . . 14
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)" |
111 | | n0i 3428 |
. . . . . . . . . . . . . 14
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112 | | biorf 744 |
. . . . . . . . . . . . . 14
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113 | 110, 111,
112 | 3syl 17 |
. . . . . . . . . . . . 13
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114 | 107, 113 | sylibrd 169 |
. . . . . . . . . . . 12
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115 | 62 | adantl 277 |
. . . . . . . . . . . . . . . . . 18
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116 | | simpl1 1000 |
. . . . . . . . . . . . . . . . . 18
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117 | 115, 116 | eqeltrrd 2255 |
. . . . . . . . . . . . . . . . 17
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    |
118 | | opelxp 4653 |
. . . . . . . . . . . . . . . . 17
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z"        |
119 | 117, 118 | sylib 122 |
. . . . . . . . . . . . . . . 16
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)" |
120 | 119 | simprd 114 |
. . . . . . . . . . . . . . 15
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121 | | pinn 7299 |
. . . . . . . . . . . . . . 15
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122 | 120, 121 | syl 14 |
. . . . . . . . . . . . . 14
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123 | | nnm0 6470 |
. . . . . . . . . . . . . 14
     |
124 | 122, 123 | syl 14 |
. . . . . . . . . . . . 13
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125 | | oveq2 5877 |
. . . . . . . . . . . . . 14
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      |
126 | 125 | eqeq1d 2186 |
. . . . . . . . . . . . 13
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127 | 124, 126 | syl5ibrcom 157 |
. . . . . . . . . . . 12
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128 | 114, 127 | syld 45 |
. . . . . . . . . . 11
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129 | | oveq2 5877 |
. . . . . . . . . . . . . . . 16
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130 | 124 | eqeq2d 2189 |
. . . . . . . . . . . . . . . 16
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131 | 129, 130 | imbitrid 154 |
. . . . . . . . . . . . . . 15
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132 | | simprlr 538 |
. . . . . . . . . . . . . . . 16
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133 | 132 | eqeq1d 2186 |
. . . . . . . . . . . . . . 15
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134 | 131, 133 | sylibrd 169 |
. . . . . . . . . . . . . 14
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135 | 119 | simpld 112 |
. . . . . . . . . . . . . . 15
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136 | | nnm00 6525 |
. . . . . . . . . . . . . . 15
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137 | 135, 103,
136 | syl2anc 411 |
. . . . . . . . . . . . . 14
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(" 
     |
138 | 134, 137 | sylibd 149 |
. . . . . . . . . . . . 13
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139 | | biorf 744 |
. . . . . . . . . . . . . . 15
 
     |
140 | | orcom 728 |
. . . . . . . . . . . . . . 15
  
    |
141 | 139, 140 | bitrdi 196 |
. . . . . . . . . . . . . 14
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     |
142 | 110, 111,
141 | 3syl 17 |
. . . . . . . . . . . . 13
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143 | 138, 142 | sylibrd 169 |
. . . . . . . . . . . 12
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144 | | oveq1 5876 |
. . . . . . . . . . . . . 14
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)"  |
145 | 144 | eqeq1d 2186 |
. . . . . . . . . . . . 13
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146 | 76, 145 | syl5ibrcom 157 |
. . . . . . . . . . . 12
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147 | 143, 146 | syld 45 |
. . . . . . . . . . 11
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148 | 128, 147 | jcad 307 |
. . . . . . . . . 10
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("        |
149 | | eqtr3 2197 |
. . . . . . . . . . 11
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150 | 149 | eqcomd 2183 |
. . . . . . . . . 10
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151 | 148, 150 | syl6 33 |
. . . . . . . . 9
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152 | | simplr 528 |
. . . . . . . . . . . . . . . . 17
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153 | 91, 152 | oveq12d 5887 |
. . . . . . . . . . . . . . . 16
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154 | 153 | adantl 277 |
. . . . . . . . . . . . . . 15
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155 | 100 | simpld 112 |
. . . . . . . . . . . . . . . . 17
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156 | | nnmcl 6476 |
. . . . . . . . . . . . . . . . 17
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157 | 155, 74, 156 | syl2anc 411 |
. . . . . . . . . . . . . . . 16
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158 | | nnmcom 6484 |
. . . . . . . . . . . . . . . . 17
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159 | 158 | adantl 277 |
. . . . . . . . . . . . . . . 16
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160 | | nnmass 6482 |
. . . . . . . . . . . . . . . . 17
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)"   |
161 | 160 | adantl 277 |
. . . . . . . . . . . . . . . 16
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("          |
162 | 157, 135,
103, 159, 161 | caov13d 6052 |
. . . . . . . . . . . . . . 15
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("             |
163 | | nnmcl 6476 |
. . . . . . . . . . . . . . . . 17
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164 | 122, 155,
163 | syl2anc 411 |
. . . . . . . . . . . . . . . 16
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165 | 161, 103,
104, 164 | caovassd 6028 |
. . . . . . . . . . . . . . 15
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166 | 154, 162,
165 | 3eqtr3d 2218 |
. . . . . . . . . . . . . 14
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      |
167 | | nnmcl 6476 |
. . . . . . . . . . . . . . . 16
           |
168 | 135, 157,
167 | syl2anc 411 |
. . . . . . . . . . . . . . 15
    
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169 | | nnmcl 6476 |
. . . . . . . . . . . . . . . 16
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170 | 104, 164,
169 | syl2anc 411 |
. . . . . . . . . . . . . . 15
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171 | | nnmcan 6514 |
. . . . . . . . . . . . . . 15
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172 | 103, 168,
170, 110, 171 | syl31anc 1241 |
. . . . . . . . . . . . . 14
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173 | 166, 172 | mpbid 147 |
. . . . . . . . . . . . 13
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)"   |
174 | 135, 155,
74, 159, 161 | caov12d 6050 |
. . . . . . . . . . . . 13
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)"   |
175 | 104, 122,
155, 159, 161 | caov13d 6052 |
. . . . . . . . . . . . 13
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)"   |
176 | 173, 174,
175 | 3eqtr3d 2218 |
. . . . . . . . . . . 12
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177 | 176 | adantr 276 |
. . . . . . . . . . 11
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178 | | nnmcl 6476 |
. . . . . . . . . . . . . 14
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179 | 135, 74, 178 | syl2anc 411 |
. . . . . . . . . . . . 13
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180 | | nnmcl 6476 |
. . . . . . . . . . . . . 14
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181 | 122, 104,
180 | syl2anc 411 |
. . . . . . . . . . . . 13
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182 | 155, 179,
181 | 3jca 1177 |
. . . . . . . . . . . 12
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183 | | nnmcan 6514 |
. . . . . . . . . . . 12
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184 | 182, 183 | sylan 283 |
. . . . . . . . . . 11
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185 | 177, 184 | mpbid 147 |
. . . . . . . . . 10
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186 | 185 | ex 115 |
. . . . . . . . 9
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187 | | 0elnn 4615 |
. . . . . . . . . 10
     |
188 | 155, 187 | syl 14 |
. . . . . . . . 9
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189 | 151, 186,
188 | mpjaod 718 |
. . . . . . . 8
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190 | 61, 65, 189 | jca32 310 |
. . . . . . 7
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191 | 190 | 2eximi 1601 |
. . . . . 6
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192 | 191 | exlimivv 1896 |
. . . . 5
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("        alt=">.
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193 | 192 | exlimivv 1896 |
. . . 4
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194 | 193 | 2eximi 1601 |
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195 | 59, 194 | syl 14 |
. 2
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196 | | 19.42vvvv 1913 |
. . 3
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197 | 5 | anbi1d 465 |
. . . . . . 7
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198 | 197 | anbi1d 465 |
. . . . . 6
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199 | 198 | 4exbidv 1870 |
. . . . 5
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200 | 4, 199 | anbi12d 473 |
. . . 4
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201 | 27 | anbi2d 464 |
. . . . 5
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202 | 29 | anbi2d 464 |
. . . . . . 7
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203 | 202 | anbi1d 465 |
. . . . . 6
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204 | 203 | 4exbidv 1870 |
. . . . 5
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205 | 201, 204 | anbi12d 473 |
. . . 4
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206 | | df-enq0 7414 |
. . . 4
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207 | 1, 19, 200, 205, 206 | brab 4269 |
. . 3
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208 | 196, 207 | bitr4i 187 |
. 2
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209 | 195, 208 | sylib 122 |
1
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