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Mirrors > Home > ILE Home > Th. List > iooshf | Unicode version |
Description: Shift the arguments of the open interval function. (Contributed by NM, 17-Aug-2008.) |
Ref | Expression |
---|---|
iooshf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltaddsub 7226 |
. . . . . 6
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2 | 1 | 3com13 1108 |
. . . . 5
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3 | 2 | 3expa 1103 |
. . . 4
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4 | 3 | adantrr 448 |
. . 3
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5 | ltsubadd 7222 |
. . . . . 6
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6 | 5 | bicomd 129 |
. . . . 5
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7 | 6 | 3expa 1103 |
. . . 4
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8 | 7 | adantrl 447 |
. . 3
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9 | 4, 8 | anbi12d 442 |
. 2
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10 | readdcl 6805 |
. . . . . 6
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11 | 10 | rexrd 6872 |
. . . . 5
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12 | 11 | ad2ant2rl 480 |
. . . 4
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13 | readdcl 6805 |
. . . . . 6
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14 | 13 | rexrd 6872 |
. . . . 5
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15 | 14 | ad2ant2l 477 |
. . . 4
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16 | rexr 6868 |
. . . . 5
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17 | 16 | ad2antrl 459 |
. . . 4
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18 | elioo5 8572 |
. . . 4
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19 | 12, 15, 17, 18 | syl3anc 1134 |
. . 3
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20 | 19 | ancoms 255 |
. 2
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21 | rexr 6868 |
. . . 4
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22 | 21 | ad2antrl 459 |
. . 3
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23 | rexr 6868 |
. . . 4
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24 | 23 | ad2antll 460 |
. . 3
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25 | resubcl 7071 |
. . . . 5
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26 | 25 | rexrd 6872 |
. . . 4
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27 | 26 | adantr 261 |
. . 3
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28 | elioo5 8572 |
. . 3
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29 | 22, 24, 27, 28 | syl3anc 1134 |
. 2
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30 | 9, 20, 29 | 3bitr4rd 210 |
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 ax-cnex 6774 ax-resscn 6775 ax-1cn 6776 ax-icn 6778 ax-addcl 6779 ax-addrcl 6780 ax-mulcl 6781 ax-addcom 6783 ax-addass 6785 ax-distr 6787 ax-i2m1 6788 ax-0id 6791 ax-rnegex 6792 ax-cnre 6794 ax-pre-ltadd 6799 |
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-nel 2204 df-ral 2305 df-rex 2306 df-reu 2307 df-rab 2309 df-v 2553 df-sbc 2759 df-dif 2914 df-un 2916 df-in 2918 df-ss 2925 df-pw 3353 df-sn 3373 df-pr 3374 df-op 3376 df-uni 3572 df-br 3756 df-opab 3810 df-id 4021 df-xp 4294 df-rel 4295 df-cnv 4296 df-co 4297 df-dm 4298 df-iota 4810 df-fun 4847 df-fv 4853 df-riota 5411 df-ov 5458 df-oprab 5459 df-mpt2 5460 df-pnf 6859 df-mnf 6860 df-xr 6861 df-ltxr 6862 df-sub 6981 df-neg 6982 df-ioo 8531 |
This theorem is referenced by: (None) |
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