Step | Hyp | Ref
| Expression |
1 | | simpl1 1000 |
. . . . . . . . 9
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2 | | simpl3 1002 |
. . . . . . . . 9
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3 | | cnprest.1 |
. . . . . . . . . 10
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4 | 3 | ntrss2 13288 |
. . . . . . . . 9
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5 | 1, 2, 4 | syl2anc 411 |
. . . . . . . 8
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6 | | simprl 529 |
. . . . . . . 8
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7 | 5, 6 | sseldd 3156 |
. . . . . . 7
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8 | | fvres 5535 |
. . . . . . 7
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9 | 7, 8 | syl 14 |
. . . . . 6
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10 | 9 | eqcomd 2183 |
. . . . 5
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11 | 10 | eleq1d 2246 |
. . . 4
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12 | | inss1 3355 |
. . . . . . . . 9
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13 | | imass2 5000 |
. . . . . . . . 9
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A"        |
14 | | sstr2 3162 |
. . . . . . . . 9
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("   
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15 | 12, 13, 14 | mp2b 8 |
. . . . . . . 8
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A"    |
16 | 15 | anim2i 342 |
. . . . . . 7
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("    
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)" |
17 | 16 | reximi 2574 |
. . . . . 6
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)" |
18 | 3 | ntropn 13284 |
. . . . . . . . . . . . 13
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19 | 1, 2, 18 | syl2anc 411 |
. . . . . . . . . . . 12
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20 | | inopn 13168 |
. . . . . . . . . . . . . 14
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21 | 20 | 3com23 1209 |
. . . . . . . . . . . . 13
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22 | 21 | 3expia 1205 |
. . . . . . . . . . . 12
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23 | 1, 19, 22 | syl2anc 411 |
. . . . . . . . . . 11
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24 | | elin 3318 |
. . . . . . . . . . . . . 14
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25 | 24 | simplbi2com 1444 |
. . . . . . . . . . . . 13
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26 | 6, 25 | syl 14 |
. . . . . . . . . . . 12
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27 | | sslin 3361 |
. . . . . . . . . . . . . 14
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28 | | imass2 5000 |
. . . . . . . . . . . . . 14
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A"    |
29 | 5, 27, 28 | 3syl 17 |
. . . . . . . . . . . . 13
    
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A"    |
30 | | sstr2 3162 |
. . . . . . . . . . . . 13
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31 | 29, 30 | syl 14 |
. . . . . . . . . . . 12
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32 | 26, 31 | anim12d 335 |
. . . . . . . . . . 11
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33 | 23, 32 | anim12d 335 |
. . . . . . . . . 10
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34 | | eleq2 2241 |
. . . . . . . . . . . 12
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35 | | imaeq2 4962 |
. . . . . . . . . . . . 13
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36 | 35 | sseq1d 3184 |
. . . . . . . . . . . 12
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37 | 34, 36 | anbi12d 473 |
. . . . . . . . . . 11
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38 | 37 | rspcev 2841 |
. . . . . . . . . 10
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39 | 33, 38 | syl6 33 |
. . . . . . . . 9
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40 | 39 | expdimp 259 |
. . . . . . . 8
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41 | 40 | rexlimdva 2594 |
. . . . . . 7
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42 | | eleq2 2241 |
. . . . . . . . 9
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43 | | imaeq2 4962 |
. . . . . . . . . 10
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)"  |
44 | 43 | sseq1d 3184 |
. . . . . . . . 9
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("   
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)"  |
45 | 42, 44 | anbi12d 473 |
. . . . . . . 8
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""      |
46 | 45 | cbvrexv 2704 |
. . . . . . 7
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47 | 41, 46 | syl6ib 161 |
. . . . . 6
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48 | 17, 47 | impbid2 143 |
. . . . 5
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A"      |
49 | | vex 2740 |
. . . . . . . 8
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_V" |
50 | 49 | inex1 4134 |
. . . . . . 7
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_V" |
51 | 50 | a1i 9 |
. . . . . 6
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52 | | uniexg 4436 |
. . . . . . . . 9
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53 | 1, 52 | syl 14 |
. . . . . . . 8
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_V"  |
54 | 2, 3 | sseqtrdi 3203 |
. . . . . . . 8
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)" |
55 | 53, 54 | ssexd 4140 |
. . . . . . 7
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56 | | elrest 12643 |
. . . . . . 7
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57 | 1, 55, 56 | syl2anc 411 |
. . . . . 6
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58 | | eleq2 2241 |
. . . . . . . 8
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59 | | elin 3318 |
. . . . . . . . . 10
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60 | 59 | rbaib 921 |
. . . . . . . . 9
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61 | 7, 60 | syl 14 |
. . . . . . . 8
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62 | 58, 61 | sylan9bbr 463 |
. . . . . . 7
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63 | | simpr 110 |
. . . . . . . . . 10
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A"   |
64 | 63 | imaeq2d 4966 |
. . . . . . . . 9
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65 | | inss2 3356 |
. . . . . . . . . 10
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66 | | resima2 4937 |
. . . . . . . . . 10
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67 | 65, 66 | ax-mp 5 |
. . . . . . . . 9
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68 | 64, 67 | eqtrdi 2226 |
. . . . . . . 8
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69 | 68 | sseq1d 3184 |
. . . . . . 7
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70 | 62, 69 | anbi12d 473 |
. . . . . 6
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71 | 51, 57, 70 | rexxfr2d 4462 |
. . . . 5
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72 | 48, 71 | bitr4d 191 |
. . . 4
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73 | 11, 72 | imbi12d 234 |
. . 3
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74 | 73 | ralbidv 2477 |
. 2
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75 | 3 | toptopon 13183 |
. . . . 5
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76 | 1, 75 | sylib 122 |
. . . 4
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77 | | simpl2 1001 |
. . . . 5
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78 | | cnprest.2 |
. . . . . 6
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79 | 78 | toptopon 13183 |
. . . . 5
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80 | 77, 79 | sylib 122 |
. . . 4
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81 | 2, 7 | sseldd 3156 |
. . . 4
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82 | | iscnp 13366 |
. . . 4
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83 | 76, 80, 81, 82 | syl3anc 1238 |
. . 3
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84 | | simprr 531 |
. . . 4
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85 | 84 | biantrurd 305 |
. . 3
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86 | 83, 85 | bitr4d 191 |
. 2
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87 | | simp1l 1021 |
. . . . . . 7
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88 | 87, 75 | sylib 122 |
. . . . . 6
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89 | | simp1r 1022 |
. . . . . 6
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90 | | resttopon 13338 |
. . . . . 6
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91 | 88, 89, 90 | syl2anc 411 |
. . . . 5
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92 | | simp3 999 |
. . . . . 6
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93 | 92, 79 | sylib 122 |
. . . . 5
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94 | 4 | 3ad2ant1 1018 |
. . . . . 6
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95 | | simp2l 1023 |
. . . . . 6
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96 | 94, 95 | sseldd 3156 |
. . . . 5
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97 | | iscnp 13366 |
. . . . 5
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98 | 91, 93, 96, 97 | syl3anc 1238 |
. . . 4
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99 | | simp2r 1024 |
. . . . . 6
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100 | 99, 89 | fssresd 5388 |
. . . . 5
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101 | 100 | biantrurd 305 |
. . . 4
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102 | 98, 101 | bitr4d 191 |
. . 3
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103 | 1, 2, 6, 84, 77, 102 | syl221anc 1249 |
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104 | 74, 86, 103 | 3bitr4d 220 |
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