Step | Hyp | Ref
| Expression |
1 | | lmcnp.3 |
. . . . . . . 8
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2 | | lmrcl 13358 |
. . . . . . . 8
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3 | 1, 2 | syl 14 |
. . . . . . 7
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4 | | toptopon2 13184 |
. . . . . . 7
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5 | 3, 4 | sylib 122 |
. . . . . 6
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6 | | lmcnp.k |
. . . . . . 7
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7 | | toptopon2 13184 |
. . . . . . 7
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8 | 6, 7 | sylib 122 |
. . . . . 6
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9 | | lmcnp.4 |
. . . . . 6
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10 | | cnpf2 13374 |
. . . . . 6
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11 | 5, 8, 9, 10 | syl3anc 1238 |
. . . . 5
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12 | | nnuz 9552 |
. . . . . . . . . 10
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13 | | 1zzd 9269 |
. . . . . . . . . 10
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14 | 5, 12, 13 | lmbr2 13381 |
. . . . . . . . 9
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15 | 1, 14 | mpbid 147 |
. . . . . . . 8
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`"             |
16 | 15 | simp1d 1009 |
. . . . . . 7
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17 | | uniexg 4436 |
. . . . . . . . 9
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18 | 3, 17 | syl 14 |
. . . . . . . 8
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19 | | cnex 7926 |
. . . . . . . 8
 |
20 | | elpm2g 6659 |
. . . . . . . 8
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21 | 18, 19, 20 | sylancl 413 |
. . . . . . 7
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22 | 16, 21 | mpbid 147 |
. . . . . 6
          |
23 | 22 | simpld 112 |
. . . . 5
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24 | | fco 5377 |
. . . . 5
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("         |
25 | 11, 23, 24 | syl2anc 411 |
. . . 4
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)"       |
26 | 25 | fdmd 5368 |
. . . . 5
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27 | 26 | feq2d 5349 |
. . . 4
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28 | 25, 27 | mpbird 167 |
. . 3
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29 | 22 | simprd 114 |
. . . 4
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30 | 26, 29 | eqsstrd 3191 |
. . 3
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31 | | uniexg 4436 |
. . . . 5
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32 | 6, 31 | syl 14 |
. . . 4
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33 | | elpm2g 6659 |
. . . 4
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)"   
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)"  |
34 | 32, 19, 33 | sylancl 413 |
. . 3
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)"   
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)"  |
35 | 28, 30, 34 | mpbir2and 944 |
. 2
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36 | 15 | simp2d 1010 |
. . 3
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)" |
37 | 11, 36 | ffvelcdmd 5648 |
. 2
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38 | 15 | simp3d 1011 |
. . . . . 6
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39 | 38 | adantr 276 |
. . . . 5
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40 | 5 | adantr 276 |
. . . . . 6
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TopOn     |
41 | 8 | adantr 276 |
. . . . . 6
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TopOn     |
42 | 36 | adantr 276 |
. . . . . 6
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43 | 9 | adantr 276 |
. . . . . 6
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44 | | simprl 529 |
. . . . . 6
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45 | | simprr 531 |
. . . . . 6
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46 | | icnpimaex 13378 |
. . . . . 6
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47 | 40, 41, 42, 43, 44, 45, 46 | syl33anc 1253 |
. . . . 5
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48 | | r19.29 2614 |
. . . . . . 7
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49 | | pm3.45 597 |
. . . . . . . . 9
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50 | 49 | imp 124 |
. . . . . . . 8
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("         |
54 | 53 | ffnd 5362 |
. . . . . . . . . . . . . . . . 17
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55 | | simplrl 535 |
. . . . . . . . . . . . . . . . . 18
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56 | | elssuni 3835 |
. . . . . . . . . . . . . . . . . 18
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U."   |
57 | 55, 56 | syl 14 |
. . . . . . . . . . . . . . . . 17
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58 | | fnfvima 5746 |
. . . . . . . . . . . . . . . . . 18
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59 | 58 | 3expia 1205 |
. . . . . . . . . . . . . . . . 17
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60 | 54, 57, 59 | syl2anc 411 |
. . . . . . . . . . . . . . . 16
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61 | 23 | ad2antrr 488 |
. . . . . . . . . . . . . . . . . 18
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62 | | fvco3 5583 |
. . . . . . . . . . . . . . . . . 18
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63 | 61, 62 | sylan 283 |
. . . . . . . . . . . . . . . . 17
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64 | 63 | eleq1d 2246 |
. . . . . . . . . . . . . . . 16
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""     |
65 | 60, 64 | sylibrd 169 |
. . . . . . . . . . . . . . 15
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66 | | simplrr 536 |
. . . . . . . . . . . . . . . 16
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v"   |
67 | 66 | sseld 3154 |
. . . . . . . . . . . . . . 15
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)"  |
68 | 65, 67 | syld 45 |
. . . . . . . . . . . . . 14
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69 | | simpr 110 |
. . . . . . . . . . . . . . 15
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70 | 26 | ad3antrrr 492 |
. . . . . . . . . . . . . . 15
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71 | 69, 70 | eleqtrrd 2257 |
. . . . . . . . . . . . . 14
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)"  |
72 | 68, 71 | jctild 316 |
. . . . . . . . . . . . 13
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73 | 72 | expimpd 363 |
. . . . . . . . . . . 12
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74 | 73 | ralimdv 2545 |
. . . . . . . . . . 11
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       

 
        |
75 | 74 | reximdv 2578 |
. . . . . . . . . 10
                              
        

 
        |
76 | 75 | expr 375 |
. . . . . . . . 9
          
                  
        

 
         |
77 | 76 | com23 78 |
. . . . . . . 8
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78 | 77 | impd 254 |
. . . . . . 7
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79 | 78 | rexlimdva 2594 |
. . . . . 6
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""        
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)"   |
80 | 52, 79 | syl5 32 |
. . . . 5
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("       
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81 | 39, 47, 80 | mp2and 433 |
. . . 4
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`"    
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82 | 81 | expr 375 |
. . 3
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83 | 82 | ralrimiva 2550 |
. 2
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84 | 8, 12, 13 | lmbr2 13381 |
. 2
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85 | 35, 37, 83, 84 | mpbir3and 1180 |
1
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