Step | Hyp | Ref
| Expression |
1 | | blrnps 13578 |
. . 3
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ball"        |
2 | | elblps 13557 |
. . . . . . 7
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("     
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y"       |
3 | | simpl1 1000 |
. . . . . . . . . . 11
   PsMet 
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`"    |
4 | | simpl2 1001 |
. . . . . . . . . . 11
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5 | | simpr 110 |
. . . . . . . . . . 11
   PsMet 
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6 | | psmetcl 13493 |
. . . . . . . . . . 11
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y"     |
7 | 3, 4, 5, 6 | syl3anc 1238 |
. . . . . . . . . 10
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y"     |
8 | | simpl3 1002 |
. . . . . . . . . 10
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9 | | qbtwnxr 10244 |
. . . . . . . . . . 11
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r"      
   |
10 | 9 | 3expia 1205 |
. . . . . . . . . 10
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11 | 7, 8, 10 | syl2anc 411 |
. . . . . . . . 9
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12 | | qre 9614 |
. . . . . . . . . . 11
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13 | | simpll1 1036 |
. . . . . . . . . . . . . . . 16
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14 | | simplr 528 |
. . . . . . . . . . . . . . . 16
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15 | | simpll2 1037 |
. . . . . . . . . . . . . . . 16
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16 | | psmetsym 13496 |
. . . . . . . . . . . . . . . 16
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17 | 13, 14, 15, 16 | syl3anc 1238 |
. . . . . . . . . . . . . . 15
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18 | | simprrl 539 |
. . . . . . . . . . . . . . 15
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19 | 17, 18 | eqbrtrd 4022 |
. . . . . . . . . . . . . 14
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20 | | simprl 529 |
. . . . . . . . . . . . . . . 16
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21 | | psmetcl 13493 |
. . . . . . . . . . . . . . . . . 18
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RR*"  |
22 | 13, 14, 15, 21 | syl3anc 1238 |
. . . . . . . . . . . . . . . . 17
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23 | | rexr 7993 |
. . . . . . . . . . . . . . . . . 18
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24 | 23 | ad2antrl 490 |
. . . . . . . . . . . . . . . . 17
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25 | 22, 24, 19 | xrltled 9786 |
. . . . . . . . . . . . . . . 16
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26 | | psmetlecl 13501 |
. . . . . . . . . . . . . . . 16
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27 | 13, 14, 15, 20, 25, 26 | syl122anc 1247 |
. . . . . . . . . . . . . . 15
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28 | | difrp 9679 |
. . . . . . . . . . . . . . 15
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29 | 27, 20, 28 | syl2anc 411 |
. . . . . . . . . . . . . 14
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)" |
30 | 19, 29 | mpbid 147 |
. . . . . . . . . . . . 13
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31 | 20, 27 | resubcld 8328 |
. . . . . . . . . . . . . . 15
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32 | 22 | xrleidd 9788 |
. . . . . . . . . . . . . . . 16
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33 | 20 | recnd 7976 |
. . . . . . . . . . . . . . . . 17
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34 | 27 | recnd 7976 |
. . . . . . . . . . . . . . . . 17
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35 | 33, 34 | nncand 8263 |
. . . . . . . . . . . . . . . 16
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36 | 32, 35 | breqtrrd 4028 |
. . . . . . . . . . . . . . 15
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37 | | blss2ps 13573 |
. . . . . . . . . . . . . . 15
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38 | 13, 14, 15, 31, 20, 36, 37 | syl33anc 1253 |
. . . . . . . . . . . . . 14
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39 | | simpll3 1038 |
. . . . . . . . . . . . . . 15
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40 | | simprrr 540 |
. . . . . . . . . . . . . . . 16
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41 | 24, 39, 40 | xrltled 9786 |
. . . . . . . . . . . . . . 15
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42 | | ssblps 13592 |
. . . . . . . . . . . . . . 15
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43 | 13, 15, 24, 39, 41, 42 | syl221anc 1249 |
. . . . . . . . . . . . . 14
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)"    |
44 | 38, 43 | sstrd 3165 |
. . . . . . . . . . . . 13
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45 | | oveq2 5877 |
. . . . . . . . . . . . . . 15
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46 | 45 | sseq1d 3184 |
. . . . . . . . . . . . . 14
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r"    |
47 | 46 | rspcev 2841 |
. . . . . . . . . . . . 13
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48 | 30, 44, 47 | syl2anc 411 |
. . . . . . . . . . . 12
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                            |
49 | 48 | expr 375 |
. . . . . . . . . . 11
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`" 
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)"             |
50 | 12, 49 | sylan2 286 |
. . . . . . . . . 10
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`" 
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)"             |
51 | 50 | rexlimdva 2594 |
. . . . . . . . 9
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)"             |
52 | 11, 51 | syld 45 |
. . . . . . . 8
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("    
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53 | 52 | expimpd 363 |
. . . . . . 7
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)"             |
54 | 2, 53 | sylbid 150 |
. . . . . 6
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("                  |
55 | | eleq2 2241 |
. . . . . . 7
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ball"     
           |
56 | | sseq2 3179 |
. . . . . . . 8
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ball"             
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("                 |
57 | 56 | rexbidv 2478 |
. . . . . . 7
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ball"      
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)"                      |
58 | 55, 57 | imbi12d 234 |
. . . . . 6
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ball"       alt="(
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59 | 54, 58 | syl5ibrcom 157 |
. . . . 5
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60 | 59 | 3expib 1206 |
. . . 4
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61 | 60 | rexlimdvv 2601 |
. . 3
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62 | 1, 61 | sylbid 150 |
. 2
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63 | 62 | 3imp 1193 |
1
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