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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 6348 |
. . . . . . . 8
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7 | fndm 5331 |
. . . . . . . 8
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8 | 6, 7 | syl 14 |
. . . . . . 7
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9 | 1, 2, 3, 4, 5 | tfrlemibacc 6346 |
. . . . . . . . . 10
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10 | 9 | unissd 3848 |
. . . . . . . . 9
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11 | 1 | recsfval 6335 |
. . . . . . . . 9
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12 | 10, 11 | sseqtrrdi 3219 |
. . . . . . . 8
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13 | dmss 4841 |
. . . . . . . 8
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14 | 12, 13 | syl 14 |
. . . . . . 7
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15 | 8, 14 | eqsstrrd 3207 |
. . . . . 6
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16 | 15 | sselda 3170 |
. . . . 5
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17 | 1 | tfrlem9 6339 |
. . . . 5
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18 | 16, 17 | syl 14 |
. . . 4
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19 | 1 | tfrlem7 6337 |
. . . . . 6
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20 | 19 | a1i 9 |
. . . . 5
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21 | 12 | adantr 276 |
. . . . 5
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22 | 8 | eleq2d 2259 |
. . . . . 6
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23 | 22 | biimpar 297 |
. . . . 5
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24 | funssfv 5557 |
. . . . 5
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25 | 20, 21, 23, 24 | syl3anc 1249 |
. . . 4
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26 | eloni 4390 |
. . . . . . . . 9
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27 | 4, 26 | syl 14 |
. . . . . . . 8
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28 | ordelss 4394 |
. . . . . . . 8
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29 | 27, 28 | sylan 283 |
. . . . . . 7
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30 | 8 | adantr 276 |
. . . . . . 7
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31 | 29, 30 | sseqtrrd 3209 |
. . . . . 6
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32 | fun2ssres 5275 |
. . . . . 6
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33 | 20, 21, 31, 32 | syl3anc 1249 |
. . . . 5
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34 | 33 | fveq2d 5535 |
. . . 4
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35 | 18, 25, 34 | 3eqtr3d 2230 |
. . 3
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36 | 35 | ralrimiva 2563 |
. 2
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37 | fveq2 5531 |
. . . 4
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38 | reseq2 4917 |
. . . . 5
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39 | 38 | fveq2d 5535 |
. . . 4
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40 | 37, 39 | eqeq12d 2204 |
. . 3
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41 | 40 | cbvralv 2718 |
. 2
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42 | 36, 41 | sylibr 134 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4189 ax-pr 4224 ax-un 4448 ax-setind 4551 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-sbc 2978 df-csb 3073 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-nul 3438 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-iun 3903 df-br 4019 df-opab 4080 df-mpt 4081 df-tr 4117 df-id 4308 df-iord 4381 df-on 4383 df-suc 4386 df-xp 4647 df-rel 4648 df-cnv 4649 df-co 4650 df-dm 4651 df-rn 4652 df-res 4653 df-iota 5193 df-fun 5234 df-fn 5235 df-f 5236 df-fv 5240 df-recs 6325 |
This theorem is referenced by: tfrlemiex 6351 |
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