Step | Hyp | Ref
| Expression |
1 | | ssrab 3233 |
. . . . 5
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2 | | simprl 529 |
. . . . . . . . 9
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~P" 
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3 | | sspwuni 3968 |
. . . . . . . . 9
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4 | 2, 3 | sylib 122 |
. . . . . . . 8
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5 | | vuniex 4435 |
. . . . . . . . 9
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6 | 5 | elpw 3580 |
. . . . . . . 8
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7 | 4, 6 | sylibr 134 |
. . . . . . 7
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8 | | eluni2 3811 |
. . . . . . . . . 10
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9 | | r19.29 2614 |
. . . . . . . . . . . . 13
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10 | | simpr 110 |
. . . . . . . . . . . . . . . 16
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11 | 10 | impr 379 |
. . . . . . . . . . . . . . 15
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12 | | elssuni 3835 |
. . . . . . . . . . . . . . . 16
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13 | 12 | adantr 276 |
. . . . . . . . . . . . . . 15
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14 | 11, 13 | eqsstrrd 3192 |
. . . . . . . . . . . . . 14
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15 | 14 | rexlimiva 2589 |
. . . . . . . . . . . . 13
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)" |
16 | 9, 15 | syl 14 |
. . . . . . . . . . . 12
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)" |
17 | 16 | ex 115 |
. . . . . . . . . . 11
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(" 
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18 | 17 | ad2antll 491 |
. . . . . . . . . 10
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19 | 8, 18 | biimtrid 152 |
. . . . . . . . 9
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U."    |
20 | 19, 4 | jctild 316 |
. . . . . . . 8
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~P" 
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21 | | eqss 3170 |
. . . . . . . 8
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U."    |
22 | 20, 21 | syl6ibr 162 |
. . . . . . 7
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23 | | eleq2 2241 |
. . . . . . . . 9
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24 | | eqeq1 2184 |
. . . . . . . . 9
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25 | 23, 24 | imbi12d 234 |
. . . . . . . 8
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26 | 25 | elrab 2893 |
. . . . . . 7
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27 | 7, 22, 26 | sylanbrc 417 |
. . . . . 6
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28 | 27 | ex 115 |
. . . . 5
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29 | 1, 28 | biimtrid 152 |
. . . 4
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30 | 29 | alrimiv 1874 |
. . 3
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31 | | inss1 3355 |
. . . . . . . . 9
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32 | | simprll 537 |
. . . . . . . . . 10
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33 | 32 | elpwid 3585 |
. . . . . . . . 9
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)" |
34 | 31, 33 | sstrid 3166 |
. . . . . . . 8
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)" |
35 | | vex 2740 |
. . . . . . . . . 10
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_V" |
36 | 35 | inex1 4134 |
. . . . . . . . 9
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_V" |
37 | 36 | elpw 3580 |
. . . . . . . 8
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)" |
38 | 34, 37 | sylibr 134 |
. . . . . . 7
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39 | | elin 3318 |
. . . . . . . 8
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40 | | simprlr 538 |
. . . . . . . . . 10
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41 | | simprrr 540 |
. . . . . . . . . 10
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42 | 40, 41 | anim12d 335 |
. . . . . . . . 9
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)"  |
43 | | ineq12 3331 |
. . . . . . . . . 10
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44 | | inidm 3344 |
. . . . . . . . . 10
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45 | 43, 44 | eqtrdi 2226 |
. . . . . . . . 9
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46 | 42, 45 | syl6 33 |
. . . . . . . 8
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47 | 39, 46 | biimtrid 152 |
. . . . . . 7
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48 | 38, 47 | jca 306 |
. . . . . 6
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49 | 48 | ex 115 |
. . . . 5
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("             |
50 | | eleq2 2241 |
. . . . . . . 8
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51 | | eqeq1 2184 |
. . . . . . . 8
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52 | 50, 51 | imbi12d 234 |
. . . . . . 7
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("       |
53 | 52 | elrab 2893 |
. . . . . 6
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54 | | eleq2 2241 |
. . . . . . . 8
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55 | | eqeq1 2184 |
. . . . . . . 8
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56 | 54, 55 | imbi12d 234 |
. . . . . . 7
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("       |
57 | 56 | elrab 2893 |
. . . . . 6
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~P" 
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58 | 53, 57 | anbi12i 460 |
. . . . 5
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59 | | eleq2 2241 |
. . . . . . 7
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60 | | eqeq1 2184 |
. . . . . . 7
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61 | 59, 60 | imbi12d 234 |
. . . . . 6
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62 | 61 | elrab 2893 |
. . . . 5
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63 | 49, 58, 62 | 3imtr4g 205 |
. . . 4
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64 | 63 | ralrimivv 2558 |
. . 3
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65 | | pwexg 4177 |
. . . . . 6
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66 | 65 | adantr 276 |
. . . . 5
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67 | | rabexg 4143 |
. . . . 5
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68 | 66, 67 | syl 14 |
. . . 4
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69 | | istopg 13164 |
. . . 4
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70 | 68, 69 | syl 14 |
. . 3
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71 | 30, 64, 70 | mpbir2and 944 |
. 2
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72 | | pwidg 3588 |
. . . . . 6
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73 | 72 | adantr 276 |
. . . . 5
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)" |
74 | | eqidd 2178 |
. . . . . 6
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75 | 74 | a1d 22 |
. . . . 5
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76 | | eleq2 2241 |
. . . . . . 7
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77 | | eqeq1 2184 |
. . . . . . 7
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78 | 76, 77 | imbi12d 234 |
. . . . . 6
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("       |
79 | 78 | elrab 2893 |
. . . . 5
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80 | 73, 75, 79 | sylanbrc 417 |
. . . 4
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81 | | elssuni 3835 |
. . . 4
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82 | 80, 81 | syl 14 |
. . 3
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83 | | ssrab2 3240 |
. . . . 5
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84 | | sspwuni 3968 |
. . . . 5
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85 | 83, 84 | mpbi 145 |
. . . 4
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86 | 85 | a1i 9 |
. . 3
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87 | 82, 86 | eqssd 3172 |
. 2
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88 | | istopon 13178 |
. 2
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89 | 71, 87, 88 | sylanbrc 417 |
1
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