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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 5883 |
. . . . . . . 8
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7 | fndm 4941 |
. . . . . . . 8
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8 | 6, 7 | syl 14 |
. . . . . . 7
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9 | 1, 2, 3, 4, 5 | tfrlemibacc 5881 |
. . . . . . . . . 10
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10 | 9 | unissd 3595 |
. . . . . . . . 9
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11 | 1 | recsfval 5872 |
. . . . . . . . 9
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12 | 10, 11 | syl6sseqr 2986 |
. . . . . . . 8
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13 | dmss 4477 |
. . . . . . . 8
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14 | 12, 13 | syl 14 |
. . . . . . 7
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15 | 8, 14 | eqsstr3d 2974 |
. . . . . 6
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16 | 15 | sselda 2939 |
. . . . 5
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17 | 1 | tfrlem9 5876 |
. . . . 5
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18 | 16, 17 | syl 14 |
. . . 4
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19 | 1 | tfrlem7 5874 |
. . . . . 6
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20 | 19 | a1i 9 |
. . . . 5
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21 | 12 | adantr 261 |
. . . . 5
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22 | 8 | eleq2d 2104 |
. . . . . 6
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23 | 22 | biimpar 281 |
. . . . 5
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24 | funssfv 5142 |
. . . . 5
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25 | 20, 21, 23, 24 | syl3anc 1134 |
. . . 4
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26 | eloni 4078 |
. . . . . . . . 9
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27 | 4, 26 | syl 14 |
. . . . . . . 8
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28 | ordelss 4082 |
. . . . . . . 8
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29 | 27, 28 | sylan 267 |
. . . . . . 7
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30 | 8 | adantr 261 |
. . . . . . 7
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31 | 29, 30 | sseqtr4d 2976 |
. . . . . 6
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32 | fun2ssres 4886 |
. . . . . 6
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33 | 20, 21, 31, 32 | syl3anc 1134 |
. . . . 5
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34 | 33 | fveq2d 5125 |
. . . 4
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35 | 18, 25, 34 | 3eqtr3d 2077 |
. . 3
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36 | 35 | ralrimiva 2386 |
. 2
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37 | fveq2 5121 |
. . . 4
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38 | reseq2 4550 |
. . . . 5
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39 | 38 | fveq2d 5125 |
. . . 4
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40 | 37, 39 | eqeq12d 2051 |
. . 3
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41 | 40 | cbvralv 2527 |
. 2
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42 | 36, 41 | sylibr 137 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-13 1401 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-sep 3866 ax-pow 3918 ax-pr 3935 ax-un 4136 ax-setind 4220 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-fal 1248 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ne 2203 df-ral 2305 df-rex 2306 df-rab 2309 df-v 2553 df-sbc 2759 df-csb 2847 df-dif 2914 df-un 2916 df-in 2918 df-ss 2925 df-nul 3219 df-pw 3353 df-sn 3373 df-pr 3374 df-op 3376 df-uni 3572 df-iun 3650 df-br 3756 df-opab 3810 df-mpt 3811 df-tr 3846 df-id 4021 df-iord 4069 df-on 4071 df-suc 4074 df-xp 4294 df-rel 4295 df-cnv 4296 df-co 4297 df-dm 4298 df-rn 4299 df-res 4300 df-iota 4810 df-fun 4847 df-fn 4848 df-f 4849 df-fv 4853 df-recs 5861 |
This theorem is referenced by: tfrlemiex 5886 |
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