Proof of Theorem tfrlemibxssdm
Step | Hyp | Ref
| Expression |
1 | | tfrlemi1.5 |
. . 3
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2 | | tfrlemi1.4 |
. . . 4
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3 | | tfrlemisucfn.2 |
. . . . . . . . . . . 12
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4 | 3 | tfrlem3-2d 6307 |
. . . . . . . . . . 11
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5 | 4 | simprd 114 |
. . . . . . . . . 10
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6 | 5 | 3ad2ant1 1018 |
. . . . . . . . 9
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7 | | vex 2740 |
. . . . . . . . . . . . 13
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_V" |
8 | | opexg 4225 |
. . . . . . . . . . . . 13
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9 | 7, 5, 8 | sylancr 414 |
. . . . . . . . . . . 12
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10 | | snidg 3620 |
. . . . . . . . . . . 12
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11 | | elun2 3303 |
. . . . . . . . . . . 12
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12 | 9, 10, 11 | 3syl 17 |
. . . . . . . . . . 11
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13 | 12 | 3ad2ant1 1018 |
. . . . . . . . . 10
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14 | | simp2r 1024 |
. . . . . . . . . . . 12
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15 | | simp3l 1025 |
. . . . . . . . . . . 12
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16 | | onelon 4381 |
. . . . . . . . . . . . . . 15
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17 | | rspe 2526 |
. . . . . . . . . . . . . . 15
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18 | 16, 17 | sylan 283 |
. . . . . . . . . . . . . 14
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19 | | tfrlemisucfn.1 |
. . . . . . . . . . . . . . 15
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)"    |
20 | | vex 2740 |
. . . . . . . . . . . . . . 15
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_V" |
21 | 19, 20 | tfrlem3a 6305 |
. . . . . . . . . . . . . 14
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22 | 18, 21 | sylibr 134 |
. . . . . . . . . . . . 13
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23 | 22 | 3adant1 1015 |
. . . . . . . . . . . 12
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24 | 14, 15, 23 | 3jca 1177 |
. . . . . . . . . . 11
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)"       |
25 | | snexg 4181 |
. . . . . . . . . . . . . 14
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26 | | unexg 4440 |
. . . . . . . . . . . . . . 15
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27 | 20, 26 | mpan 424 |
. . . . . . . . . . . . . 14
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28 | 9, 25, 27 | 3syl 17 |
. . . . . . . . . . . . 13
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29 | | isset 2743 |
. . . . . . . . . . . . 13
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>."    |
30 | 28, 29 | sylib 122 |
. . . . . . . . . . . 12
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31 | 30 | 3ad2ant1 1018 |
. . . . . . . . . . 11
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)"                 |
32 | | simpr3 1005 |
. . . . . . . . . . . . . . 15
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33 | | 19.8a 1590 |
. . . . . . . . . . . . . . . 16
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34 | | rspe 2526 |
. . . . . . . . . . . . . . . . 17
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35 | | tfrlemi1.3 |
. . . . . . . . . . . . . . . . . 18
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36 | 35 | abeq2i 2288 |
. . . . . . . . . . . . . . . . 17
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37 | 34, 36 | sylibr 134 |
. . . . . . . . . . . . . . . 16
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38 | 33, 37 | sylan2 286 |
. . . . . . . . . . . . . . 15
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39 | 32, 38 | eqeltrrd 2255 |
. . . . . . . . . . . . . 14
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40 | 39 | 3exp2 1225 |
. . . . . . . . . . . . 13
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)"    |
41 | 40 | 3imp 1193 |
. . . . . . . . . . . 12
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>."     |
42 | 41 | exlimdv 1819 |
. . . . . . . . . . 11
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43 | 24, 31, 42 | sylc 62 |
. . . . . . . . . 10
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44 | | elunii 3812 |
. . . . . . . . . 10
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45 | 13, 43, 44 | syl2anc 411 |
. . . . . . . . 9
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46 | | opeq2 3777 |
. . . . . . . . . . . 12
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47 | 46 | eleq1d 2246 |
. . . . . . . . . . 11
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)"     |
48 | 47 | spcegv 2825 |
. . . . . . . . . 10
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U."    |
49 | 7 | eldm2 4821 |
. . . . . . . . . 10
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50 | 48, 49 | syl6ibr 162 |
. . . . . . . . 9
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51 | 6, 45, 50 | sylc 62 |
. . . . . . . 8
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                   |
52 | 51 | 3expia 1205 |
. . . . . . 7
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     
               |
53 | 52 | exlimdv 1819 |
. . . . . 6
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                       |
54 | 53 | anassrs 400 |
. . . . 5
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55 | 54 | ralimdva 2544 |
. . . 4
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)"  |
56 | 2, 55 | mpdan 421 |
. . 3
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)"  
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)"  |
57 | 1, 56 | mpd 13 |
. 2
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)" |
58 | | dfss3 3145 |
. 2
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59 | 57, 58 | sylibr 134 |
1
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)" |