Step | Hyp | Ref
| Expression |
1 | | axcaucvg.n |
. . . 4
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2 | | axcaucvg.f |
. . . 4
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3 | | axcaucvg.cau |
. . . 4
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4 | | axcaucvg.g |
. . . 4
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5 | 1, 2, 3, 4 | axcaucvglemf 7886 |
. . 3
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6 | 1, 2, 3, 4 | axcaucvglemcau 7888 |
. . 3
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7 | 5, 6 | caucvgsr 7792 |
. 2
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8 | | opelreal 7817 |
. . . . 5
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9 | 8 | biimpri 133 |
. . . 4
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10 | 9 | ad2antrl 490 |
. . 3
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)"       
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11 | | breq2 4004 |
. . . . . . . . . 10
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12 | | fveq2 5511 |
. . . . . . . . . . . 12
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`"        |
13 | 12 | breq1d 4010 |
. . . . . . . . . . 11
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14 | 12 | oveq1d 5884 |
. . . . . . . . . . . 12
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15 | 14 | breq2d 4012 |
. . . . . . . . . . 11
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16 | 13, 15 | anbi12d 473 |
. . . . . . . . . 10
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("                    
          |
17 | 11, 16 | imbi12d 234 |
. . . . . . . . 9
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18 | 17 | cbvralv 2703 |
. . . . . . . 8
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19 | 18 | rexbii 2484 |
. . . . . . 7
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20 | 19 | imbi2i 226 |
. . . . . 6
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21 | 20 | ralbii 2483 |
. . . . 5
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22 | 21 | anbi2i 457 |
. . . 4
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23 | | elreal 7818 |
. . . . . . . . 9
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24 | 23 | biimpi 120 |
. . . . . . . 8
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25 | 24 | ad2antlr 489 |
. . . . . . 7
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26 | | simplrr 536 |
. . . . . . . . . . 11
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27 | 26 | ad2antrr 488 |
. . . . . . . . . 10
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28 | | simprr 531 |
. . . . . . . . . . 11
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29 | | simplr 528 |
. . . . . . . . . . 11
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e"      |
30 | | breq2 4004 |
. . . . . . . . . . . . 13
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31 | | df-0 7809 |
. . . . . . . . . . . . . . 15
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32 | 31 | breq1i 4007 |
. . . . . . . . . . . . . 14
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33 | | ltresr 7829 |
. . . . . . . . . . . . . 14
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34 | 32, 33 | bitri 184 |
. . . . . . . . . . . . 13
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35 | 30, 34 | bitr3di 195 |
. . . . . . . . . . . 12
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36 | 35 | biimpa 296 |
. . . . . . . . . . 11
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37 | 28, 29, 36 | syl2anc 411 |
. . . . . . . . . 10
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e"      |
38 | | breq2 4004 |
. . . . . . . . . . . . 13
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39 | | oveq2 5877 |
. . . . . . . . . . . . . . . . 17
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40 | 39 | breq2d 4012 |
. . . . . . . . . . . . . . . 16
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41 | | oveq2 5877 |
. . . . . . . . . . . . . . . . 17
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42 | 41 | breq2d 4012 |
. . . . . . . . . . . . . . . 16
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43 | 40, 42 | anbi12d 473 |
. . . . . . . . . . . . . . 15
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44 | 43 | imbi2d 230 |
. . . . . . . . . . . . . 14
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45 | 44 | rexralbidv 2503 |
. . . . . . . . . . . . 13
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)" 
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46 | 38, 45 | imbi12d 234 |
. . . . . . . . . . . 12
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("           |
47 | 46 | rspcv 2837 |
. . . . . . . . . . 11
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48 | 47 | ad2antrl 490 |
. . . . . . . . . 10
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49 | 27, 37, 48 | mp2d 47 |
. . . . . . . . 9
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50 | | breq1 4003 |
. . . . . . . . . . . 12
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51 | 50 | imbi1d 231 |
. . . . . . . . . . 11
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52 | 51 | ralbidv 2477 |
. . . . . . . . . 10
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53 | 52 | cbvrexv 2704 |
. . . . . . . . 9
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54 | 49, 53 | sylib 122 |
. . . . . . . 8
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55 | | pitonn 7838 |
. . . . . . . . . . 11
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56 | 55, 1 | eleqtrrdi 2271 |
. . . . . . . . . 10
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57 | 56 | ad2antrl 490 |
. . . . . . . . 9
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58 | 1 | nntopi 7884 |
. . . . . . . . . . . 12
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59 | 58 | adantl 277 |
. . . . . . . . . . 11
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60 | | breq2 4004 |
. . . . . . . . . . . . . 14
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61 | | fveq2 5511 |
. . . . . . . . . . . . . . . 16
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62 | 61 | breq1d 4010 |
. . . . . . . . . . . . . . 15
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63 | 61 | oveq1d 5884 |
. . . . . . . . . . . . . . . 16
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64 | 63 | breq2d 4012 |
. . . . . . . . . . . . . . 15
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65 | 62, 64 | anbi12d 473 |
. . . . . . . . . . . . . 14
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66 | 60, 65 | imbi12d 234 |
. . . . . . . . . . . . 13
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67 | | simplrr 536 |
. . . . . . . . . . . . . 14
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69 | | simprl 529 |
. . . . . . . . . . . . 13
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70 | 66, 68, 69 | rspcdva 2846 |
. . . . . . . . . . . 12
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71 | | simplrl 535 |
. . . . . . . . . . . . . . 15
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73 | | ltrennb 7844 |
. . . . . . . . . . . . . 14
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74 | 72, 69, 73 | syl2anc 411 |
. . . . . . . . . . . . 13
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76 | 75 | breq2d 4012 |
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77 | 74, 76 | bitrd 188 |
. . . . . . . . . . . 12
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78 | | ltresr 7829 |
. . . . . . . . . . . . . 14
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79 | | simplll 533 |
. . . . . . . . . . . . . . . . . 18
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80 | 79 | ad4antr 494 |
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81 | 1, 2, 3, 4 | axcaucvglemval 7887 |
. . . . . . . . . . . . . . . . 17
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82 | 80, 69, 81 | syl2anc 411 |
. . . . . . . . . . . . . . . 16
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84 | 82, 83 | eqtr3d 2212 |
. . . . . . . . . . . . . . 15
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85 | | simplrl 535 |
. . . . . . . . . . . . . . . . . 18
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86 | 85 | ad5antr 496 |
. . . . . . . . . . . . . . . . 17
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87 | | simplrl 535 |
. . . . . . . . . . . . . . . . . 18
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89 | | addresr 7827 |
. . . . . . . . . . . . . . . . 17
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90 | 86, 88, 89 | syl2anc 411 |
. . . . . . . . . . . . . . . 16
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91 | 28 | oveq2d 5885 |
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92 | 91 | ad3antrrr 492 |
. . . . . . . . . . . . . . . 16
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93 | 90, 92 | eqtr3d 2212 |
. . . . . . . . . . . . . . 15
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96 | | ltresr 7829 |
. . . . . . . . . . . . . 14
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97 | 80, 5 | syl 14 |
. . . . . . . . . . . . . . . . . 18
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99 | | addresr 7827 |
. . . . . . . . . . . . . . . . 17
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100 | 98, 88, 99 | syl2anc 411 |
. . . . . . . . . . . . . . . 16
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103 | 100, 102 | eqtr3d 2212 |
. . . . . . . . . . . . . . 15
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104 | 103 | breq2d 4012 |
. . . . . . . . . . . . . 14
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105 | 96, 104 | bitr3id 194 |
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106 | 95, 105 | anbi12d 473 |
. . . . . . . . . . . 12
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107 | 70, 77, 106 | 3imtr3d 202 |
. . . . . . . . . . 11
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108 | 59, 107 | rexlimddv 2599 |
. . . . . . . . . 10
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109 | 108 | ralrimiva 2550 |
. . . . . . . . 9
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110 | | breq1 4003 |
. . . . . . . . . . . 12
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111 | 110 | imbi1d 231 |
. . . . . . . . . . 11
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112 | 111 | ralbidv 2477 |
. . . . . . . . . 10
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113 | 112 | rspcev 2841 |
. . . . . . . . 9
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114 | 57, 109, 113 | syl2anc 411 |
. . . . . . . 8
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115 | 54, 114 | rexlimddv 2599 |
. . . . . . 7
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b"                |
116 | 25, 115 | rexlimddv 2599 |
. . . . . 6
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117 | 116 | ex 115 |
. . . . 5
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118 | 117 | ralrimiva 2550 |
. . . 4
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119 | 22, 118 | sylan2br 288 |
. . 3
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b"                 |
120 | | oveq1 5876 |
. . . . . . . . . 10
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<."      |
121 | 120 | breq2d 4012 |
. . . . . . . . 9
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122 | | breq1 4003 |
. . . . . . . . 9
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)"   |
123 | 121, 122 | anbi12d 473 |
. . . . . . . 8
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124 | 123 | imbi2d 230 |
. . . . . . 7
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)"     |
125 | 124 | rexralbidv 2503 |
. . . . . 6
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126 | 125 | imbi2d 230 |
. . . . 5
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127 | 126 | ralbidv 2477 |
. . . 4
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128 | 127 | rspcev 2841 |
. . 3
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129 | 10, 119, 128 | syl2anc 411 |
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130 | 7, 129 | rexlimddv 2599 |
1
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