Step | Hyp | Ref
| Expression |
1 | | df-tpos 6240 |
. . 3
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2 | | relcnv 5002 |
. . . . . . 7
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3 | | df-rel 4630 |
. . . . . . 7
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4 | 2, 3 | mpbi 145 |
. . . . . 6
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5 | | unss1 3304 |
. . . . . 6
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6 | | resmpt 4951 |
. . . . . 6
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7 | 4, 5, 6 | mp2b 8 |
. . . . 5
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8 | | resss 4927 |
. . . . 5
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9 | 7, 8 | eqsstrri 3188 |
. . . 4
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10 | | coss2 4779 |
. . . 4
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11 | 9, 10 | ax-mp 5 |
. . 3
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12 | 1, 11 | eqsstri 3187 |
. 2
tpos 
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13 | | relco 5123 |
. . 3
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14 | | vex 2740 |
. . . . 5
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_V" |
15 | | vex 2740 |
. . . . 5
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_V" |
16 | 14, 15 | opelco 4795 |
. . . 4
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y"                       
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17 | | vex 2740 |
. . . . . . . . 9
 |
18 | | eleq1 2240 |
. . . . . . . . . 10
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19 | | sneq 3602 |
. . . . . . . . . . . . 13
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    |
20 | 19 | cnveqd 4799 |
. . . . . . . . . . . 12
         |
21 | 20 | unieqd 3818 |
. . . . . . . . . . 11
           |
22 | 21 | eqeq2d 2189 |
. . . . . . . . . 10
     
       |
23 | 18, 22 | anbi12d 473 |
. . . . . . . . 9
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("   
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("   
           |
24 | | eqeq1 2184 |
. . . . . . . . . 10
     
       |
25 | 24 | anbi2d 464 |
. . . . . . . . 9
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("   
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26 | | df-mpt 4063 |
. . . . . . . . 9
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x"    |
27 | 14, 17, 23, 25, 26 | brab 4269 |
. . . . . . . 8
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U."       |
28 | | simplr 528 |
. . . . . . . . . . . 12
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29 | 17, 15 | breldm 4827 |
. . . . . . . . . . . . 13
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30 | 29 | adantl 277 |
. . . . . . . . . . . 12
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  |
31 | 28, 30 | eqeltrrd 2255 |
. . . . . . . . . . 11
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y"   |
32 | | elvv 4685 |
. . . . . . . . . . . . . 14
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33 | | opswapg 5111 |
. . . . . . . . . . . . . . . . . . 19
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)" |
34 | 15, 17, 33 | mp2an 426 |
. . . . . . . . . . . . . . . . . 18
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35 | 34 | eleq1i 2243 |
. . . . . . . . . . . . . . . . 17
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w"    |
36 | 15, 17 | opelcnv 4805 |
. . . . . . . . . . . . . . . . 17
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z"  
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37 | 35, 36 | bitr4i 187 |
. . . . . . . . . . . . . . . 16
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z"     |
38 | | sneq 3602 |
. . . . . . . . . . . . . . . . . . . 20
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39 | 38 | cnveqd 4799 |
. . . . . . . . . . . . . . . . . . 19
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40 | 39 | unieqd 3818 |
. . . . . . . . . . . . . . . . . 18
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41 | 40 | eleq1d 2246 |
. . . . . . . . . . . . . . . . 17
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42 | | eleq1 2240 |
. . . . . . . . . . . . . . . . 17
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43 | 41, 42 | bibi12d 235 |
. . . . . . . . . . . . . . . 16
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z"       |
44 | 37, 43 | mpbiri 168 |
. . . . . . . . . . . . . . 15
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45 | 44 | exlimivv 1896 |
. . . . . . . . . . . . . 14
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46 | 32, 45 | sylbi 121 |
. . . . . . . . . . . . 13
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47 | 46 | biimpcd 159 |
. . . . . . . . . . . 12
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48 | | elun1 3302 |
. . . . . . . . . . . 12
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}"   |
49 | 47, 48 | syl6 33 |
. . . . . . . . . . 11
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}"    |
50 | 31, 49 | syl 14 |
. . . . . . . . . 10
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}"    |
51 | | elun2 3303 |
. . . . . . . . . . 11
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52 | 51 | a1i 9 |
. . . . . . . . . 10
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53 | | simpll 527 |
. . . . . . . . . . 11
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54 | | elun 3276 |
. . . . . . . . . . 11
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55 | 53, 54 | sylib 122 |
. . . . . . . . . 10
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56 | 50, 52, 55 | mpjaod 718 |
. . . . . . . . 9
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}"   |
57 | | simpr 110 |
. . . . . . . . . 10
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    |
58 | 28, 57 | eqbrtrrd 4024 |
. . . . . . . . 9
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y"     |
59 | 56, 58 | jca 306 |
. . . . . . . 8
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z"   |
60 | 27, 59 | sylanb 284 |
. . . . . . 7
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}"          |
61 | | brtpos2 6246 |
. . . . . . . 8
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z"    |
62 | 15, 61 | ax-mp 5 |
. . . . . . 7
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F"
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z"   |
63 | 60, 62 | sylibr 134 |
. . . . . 6
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64 | | df-br 4001 |
. . . . . 6
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65 | 63, 64 | sylib 122 |
. . . . 5
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66 | 65 | exlimiv 1598 |
. . . 4
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67 | 16, 66 | sylbi 121 |
. . 3
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68 | 13, 67 | relssi 4714 |
. 2
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69 | 12, 68 | eqssi 3171 |
1
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