Step | Hyp | Ref
| Expression |
1 | | elfzoelz 10133 |
. . . . . 6
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2 | | crth.1 |
. . . . . 6
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3 | 1, 2 | eleq2s 2272 |
. . . . 5
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4 | | simpr 110 |
. . . . . . . 8
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5 | | crth.4 |
. . . . . . . . . 10
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6 | 5 | simp1d 1009 |
. . . . . . . . 9
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7 | 6 | adantr 276 |
. . . . . . . 8
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8 | | zmodfzo 10333 |
. . . . . . . 8
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9 | 4, 7, 8 | syl2anc 411 |
. . . . . . 7
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10 | 5 | simp2d 1010 |
. . . . . . . . 9
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11 | 10 | adantr 276 |
. . . . . . . 8
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12 | | zmodfzo 10333 |
. . . . . . . 8
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13 | 4, 11, 12 | syl2anc 411 |
. . . . . . 7
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14 | | opelxpi 4655 |
. . . . . . 7
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15 | 9, 13, 14 | syl2anc 411 |
. . . . . 6
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16 | | crth.2 |
. . . . . 6
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17 | 15, 16 | eleqtrrdi 2271 |
. . . . 5
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18 | 3, 17 | sylan2 286 |
. . . 4
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19 | | crth.3 |
. . . 4
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20 | 18, 19 | fmptd 5666 |
. . 3
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21 | | simprl 529 |
. . . . . . . 8
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22 | | elfzoelz 10133 |
. . . . . . . . . . . . 13
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23 | 22, 2 | eleq2s 2272 |
. . . . . . . . . . . 12
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24 | 23 | ad2antrl 490 |
. . . . . . . . . . 11
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25 | | zq 9615 |
. . . . . . . . . . 11
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26 | 24, 25 | syl 14 |
. . . . . . . . . 10
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27 | 6 | adantr 276 |
. . . . . . . . . . 11
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28 | | nnq 9622 |
. . . . . . . . . . 11
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29 | 27, 28 | syl 14 |
. . . . . . . . . 10
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30 | 27 | nngt0d 8952 |
. . . . . . . . . 10
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31 | 26, 29, 30 | modqcld 10314 |
. . . . . . . . 9
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32 | 10 | adantr 276 |
. . . . . . . . . . 11
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33 | | nnq 9622 |
. . . . . . . . . . 11
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34 | 32, 33 | syl 14 |
. . . . . . . . . 10
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35 | 32 | nngt0d 8952 |
. . . . . . . . . 10
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36 | 26, 34, 35 | modqcld 10314 |
. . . . . . . . 9
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("    |
37 | | opexg 4225 |
. . . . . . . . 9
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M"       |
38 | 31, 36, 37 | syl2anc 411 |
. . . . . . . 8
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)"      |
39 | | oveq1 5876 |
. . . . . . . . . 10
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M"   |
40 | | oveq1 5876 |
. . . . . . . . . 10
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41 | 39, 40 | opeq12d 3784 |
. . . . . . . . 9
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N"    |
42 | 41, 19 | fvmptg 5588 |
. . . . . . . 8
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43 | 21, 38, 42 | syl2anc 411 |
. . . . . . 7
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N"    |
44 | | simprr 531 |
. . . . . . . 8
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45 | | elfzoelz 10133 |
. . . . . . . . . . . . 13
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46 | 45, 2 | eleq2s 2272 |
. . . . . . . . . . . 12
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47 | 44, 46 | syl 14 |
. . . . . . . . . . 11
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48 | | zq 9615 |
. . . . . . . . . . 11
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49 | 47, 48 | syl 14 |
. . . . . . . . . 10
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50 | 49, 29, 30 | modqcld 10314 |
. . . . . . . . 9
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("    |
51 | 49, 34, 35 | modqcld 10314 |
. . . . . . . . 9
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("    |
52 | | opexg 4225 |
. . . . . . . . 9
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M"       |
53 | 50, 51, 52 | syl2anc 411 |
. . . . . . . 8
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)"      |
54 | | oveq1 5876 |
. . . . . . . . . 10
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M"   |
55 | | oveq1 5876 |
. . . . . . . . . 10
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N"   |
56 | 54, 55 | opeq12d 3784 |
. . . . . . . . 9
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N"    |
57 | 56, 19 | fvmptg 5588 |
. . . . . . . 8
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M"         |
59 | 43, 58 | eqeq12d 2192 |
. . . . . 6
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M"            |
63 | 27 | nnzd 9363 |
. . . . . . 7
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64 | 32 | nnzd 9363 |
. . . . . . 7
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65 | 21, 2 | eleqtrdi 2270 |
. . . . . . . . 9
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66 | 65, 22 | syl 14 |
. . . . . . . 8
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67 | 44, 2 | eleqtrdi 2270 |
. . . . . . . . 9
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)"   |
68 | 67, 45 | syl 14 |
. . . . . . . 8
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69 | 66, 68 | zsubcld 9369 |
. . . . . . 7
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("    |
70 | 5 | simp3d 1011 |
. . . . . . . 8
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71 | 70 | adantr 276 |
. . . . . . 7
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("    |
72 | | coprmdvds2 12076 |
. . . . . . 7
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)"   |
73 | 63, 64, 69, 71, 72 | syl31anc 1241 |
. . . . . 6
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74 | | moddvds 11790 |
. . . . . . . 8
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75 | 27, 66, 68, 74 | syl3anc 1238 |
. . . . . . 7
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76 | | moddvds 11790 |
. . . . . . . 8
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77 | 32, 66, 68, 76 | syl3anc 1238 |
. . . . . . 7
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78 | 75, 77 | anbi12d 473 |
. . . . . 6
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79 | | qmulcl 9626 |
. . . . . . . . . 10
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80 | 29, 34, 79 | syl2anc 411 |
. . . . . . . . 9
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81 | | elfzole1 10141 |
. . . . . . . . . 10
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82 | 65, 81 | syl 14 |
. . . . . . . . 9
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83 | | elfzolt2 10142 |
. . . . . . . . . 10
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    |
84 | 65, 83 | syl 14 |
. . . . . . . . 9
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85 | | modqid 10335 |
. . . . . . . . 9
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86 | 26, 80, 82, 84, 85 | syl22anc 1239 |
. . . . . . . 8
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87 | | elfzole1 10141 |
. . . . . . . . . 10
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88 | 67, 87 | syl 14 |
. . . . . . . . 9
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89 | | elfzolt2 10142 |
. . . . . . . . . 10
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    |
90 | 67, 89 | syl 14 |
. . . . . . . . 9
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91 | | modqid 10335 |
. . . . . . . . 9
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     |
92 | 49, 80, 88, 90, 91 | syl22anc 1239 |
. . . . . . . 8
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93 | 86, 92 | eqeq12d 2192 |
. . . . . . 7
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94 | 27, 32 | nnmulcld 8957 |
. . . . . . . 8
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95 | | moddvds 11790 |
. . . . . . . 8
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96 | 94, 66, 68, 95 | syl3anc 1238 |
. . . . . . 7
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97 | 93, 96 | bitr3d 190 |
. . . . . 6
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98 | 73, 78, 97 | 3imtr4d 203 |
. . . . 5
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99 | 62, 98 | sylbid 150 |
. . . 4
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100 | 99 | ralrimivva 2559 |
. . 3
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101 | | dff13 5763 |
. . 3
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102 | 20, 100, 101 | sylanbrc 417 |
. 2
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)" |
103 | | nnnn0 9172 |
. . . . . 6
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104 | | nnnn0 9172 |
. . . . . 6
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105 | | hashfzo0 10787 |
. . . . . . . . 9
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♯  ..^    |
106 | | hashfzo0 10787 |
. . . . . . . . 9
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♯  ..^    |
107 | 105, 106 | oveqan12d 5888 |
. . . . . . . 8
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(" ♯  ..^  ♯  ..^       |
108 | | 0z 9253 |
. . . . . . . . . 10
 |
109 | | simpl 109 |
. . . . . . . . . . 11
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110 | 109 | nn0zd 9362 |
. . . . . . . . . 10
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111 | | fzofig 10418 |
. . . . . . . . . 10
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  ..^   |
112 | 108, 110,
111 | sylancr 414 |
. . . . . . . . 9
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(" ..^   |
113 | | nn0z 9262 |
. . . . . . . . . . 11
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114 | 113 | adantl 277 |
. . . . . . . . . 10
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115 | | fzofig 10418 |
. . . . . . . . . 10
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116 | 108, 114,
115 | sylancr 414 |
. . . . . . . . 9
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117 | | hashxp 10790 |
. . . . . . . . 9
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118 | 112, 116,
117 | syl2anc 411 |
. . . . . . . 8
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119 | | nn0mulcl 9201 |
. . . . . . . . 9
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("    |
120 | | hashfzo0 10787 |
. . . . . . . . 9
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121 | 119, 120 | syl 14 |
. . . . . . . 8
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122 | 107, 118,
121 | 3eqtr4rd 2221 |
. . . . . . 7
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123 | 119 | nn0zd 9362 |
. . . . . . . . 9
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     |
124 | | fzofig 10418 |
. . . . . . . . 9
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   ..^     |
125 | 108, 123,
124 | sylancr 414 |
. . . . . . . 8
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126 | | xpfi 6923 |
. . . . . . . . 9
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127 | 112, 116,
126 | syl2anc 411 |
. . . . . . . 8
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128 | | hashen 10748 |
. . . . . . . 8
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(" ..^  ..^     |
129 | 125, 127,
128 | syl2anc 411 |
. . . . . . 7
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(" ♯  ..^    ♯   alt="(
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130 | 122, 129 | mpbid 147 |
. . . . . 6
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131 | 103, 104,
130 | syl2an 289 |
. . . . 5
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  ..^     ..^  ..^    |
132 | 6, 10, 131 | syl2anc 411 |
. . . 4
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133 | 132, 2, 16 | 3brtr4g 4034 |
. . 3
   |
134 | 6 | nnnn0d 9218 |
. . . . 5
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135 | 10 | nnnn0d 9218 |
. . . . 5
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136 | 134, 135,
127 | syl2anc 411 |
. . . 4
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Fin"  |
137 | 16, 136 | eqeltrid 2264 |
. . 3
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138 | | f1finf1o 6940 |
. . 3
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F"       |
139 | 133, 137,
138 | syl2anc 411 |
. 2
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F"       |
140 | 102, 139 | mpbid 147 |
1
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