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Mirrors > Home > ILE Home > Th. List > tfrlemiubacc | Unicode version |
Description: The union of ![]() |
Ref | Expression |
---|---|
tfrlemisucfn.1 |
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tfrlemisucfn.2 |
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tfrlemi1.3 |
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tfrlemi1.4 |
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tfrlemi1.5 |
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Ref | Expression |
---|---|
tfrlemiubacc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfrlemisucfn.1 |
. . . . . . . . 9
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2 | tfrlemisucfn.2 |
. . . . . . . . 9
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3 | tfrlemi1.3 |
. . . . . . . . 9
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4 | tfrlemi1.4 |
. . . . . . . . 9
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5 | tfrlemi1.5 |
. . . . . . . . 9
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6 | 1, 2, 3, 4, 5 | tfrlemibfn 6233 |
. . . . . . . 8
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7 | fndm 5230 |
. . . . . . . 8
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8 | 6, 7 | syl 14 |
. . . . . . 7
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9 | 1, 2, 3, 4, 5 | tfrlemibacc 6231 |
. . . . . . . . . 10
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10 | 9 | unissd 3768 |
. . . . . . . . 9
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11 | 1 | recsfval 6220 |
. . . . . . . . 9
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12 | 10, 11 | sseqtrrdi 3151 |
. . . . . . . 8
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13 | dmss 4746 |
. . . . . . . 8
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14 | 12, 13 | syl 14 |
. . . . . . 7
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15 | 8, 14 | eqsstrrd 3139 |
. . . . . 6
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16 | 15 | sselda 3102 |
. . . . 5
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17 | 1 | tfrlem9 6224 |
. . . . 5
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18 | 16, 17 | syl 14 |
. . . 4
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19 | 1 | tfrlem7 6222 |
. . . . . 6
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20 | 19 | a1i 9 |
. . . . 5
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21 | 12 | adantr 274 |
. . . . 5
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22 | 8 | eleq2d 2210 |
. . . . . 6
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23 | 22 | biimpar 295 |
. . . . 5
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24 | funssfv 5455 |
. . . . 5
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25 | 20, 21, 23, 24 | syl3anc 1217 |
. . . 4
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26 | eloni 4305 |
. . . . . . . . 9
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27 | 4, 26 | syl 14 |
. . . . . . . 8
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28 | ordelss 4309 |
. . . . . . . 8
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29 | 27, 28 | sylan 281 |
. . . . . . 7
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30 | 8 | adantr 274 |
. . . . . . 7
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31 | 29, 30 | sseqtrrd 3141 |
. . . . . 6
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32 | fun2ssres 5174 |
. . . . . 6
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33 | 20, 21, 31, 32 | syl3anc 1217 |
. . . . 5
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34 | 33 | fveq2d 5433 |
. . . 4
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35 | 18, 25, 34 | 3eqtr3d 2181 |
. . 3
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36 | 35 | ralrimiva 2508 |
. 2
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37 | fveq2 5429 |
. . . 4
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38 | reseq2 4822 |
. . . . 5
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39 | 38 | fveq2d 5433 |
. . . 4
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40 | 37, 39 | eqeq12d 2155 |
. . 3
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41 | 40 | cbvralv 2657 |
. 2
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42 | 36, 41 | sylibr 133 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-un 4363 ax-setind 4460 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ne 2310 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-sbc 2914 df-csb 3008 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-nul 3369 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-iun 3823 df-br 3938 df-opab 3998 df-mpt 3999 df-tr 4035 df-id 4223 df-iord 4296 df-on 4298 df-suc 4301 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-res 4559 df-iota 5096 df-fun 5133 df-fn 5134 df-f 5135 df-fv 5139 df-recs 6210 |
This theorem is referenced by: tfrlemiex 6236 |
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