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Mirrors > Home > ILE Home > Th. List > iccshftr | Unicode version |
Description: Membership in a shifted interval. (Contributed by Jeff Madsen, 2-Sep-2009.) |
Ref | Expression |
---|---|
iccshftr.1 | |
iccshftr.2 |
Ref | Expression |
---|---|
iccshftr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 102 | . . . . 5 | |
2 | readdcl 7007 | . . . . 5 | |
3 | 1, 2 | 2thd 164 | . . . 4 |
4 | 3 | adantl 262 | . . 3 |
5 | leadd1 7425 | . . . . . 6 | |
6 | 5 | 3expb 1105 | . . . . 5 |
7 | 6 | adantlr 446 | . . . 4 |
8 | iccshftr.1 | . . . . 5 | |
9 | 8 | breq1i 3771 | . . . 4 |
10 | 7, 9 | syl6bb 185 | . . 3 |
11 | leadd1 7425 | . . . . . . 7 | |
12 | 11 | 3expb 1105 | . . . . . 6 |
13 | 12 | an12s 499 | . . . . 5 |
14 | 13 | adantll 445 | . . . 4 |
15 | iccshftr.2 | . . . . 5 | |
16 | 15 | breq2i 3772 | . . . 4 |
17 | 14, 16 | syl6bb 185 | . . 3 |
18 | 4, 10, 17 | 3anbi123d 1207 | . 2 |
19 | elicc2 8807 | . . 3 | |
20 | 19 | adantr 261 | . 2 |
21 | readdcl 7007 | . . . . . 6 | |
22 | 8, 21 | syl5eqelr 2125 | . . . . 5 |
23 | readdcl 7007 | . . . . . 6 | |
24 | 15, 23 | syl5eqelr 2125 | . . . . 5 |
25 | elicc2 8807 | . . . . 5 | |
26 | 22, 24, 25 | syl2an 273 | . . . 4 |
27 | 26 | anandirs 527 | . . 3 |
28 | 27 | adantrl 447 | . 2 |
29 | 18, 20, 28 | 3bitr4d 209 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 w3a 885 wceq 1243 wcel 1393 class class class wbr 3764 (class class class)co 5512 cr 6888 caddc 6892 cle 7061 cicc 8760 |
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 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-13 1404 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 ax-un 4170 ax-setind 4262 ax-cnex 6975 ax-resscn 6976 ax-1cn 6977 ax-icn 6979 ax-addcl 6980 ax-addrcl 6981 ax-mulcl 6982 ax-addcom 6984 ax-addass 6986 ax-i2m1 6989 ax-0id 6992 ax-rnegex 6993 ax-pre-ltirr 6996 ax-pre-ltwlin 6997 ax-pre-lttrn 6998 ax-pre-ltadd 7000 |
This theorem depends on definitions: df-bi 110 df-3or 886 df-3an 887 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ne 2206 df-nel 2207 df-ral 2311 df-rex 2312 df-rab 2315 df-v 2559 df-sbc 2765 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-id 4030 df-po 4033 df-iso 4034 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-iota 4867 df-fun 4904 df-fv 4910 df-ov 5515 df-oprab 5516 df-mpt2 5517 df-pnf 7062 df-mnf 7063 df-xr 7064 df-ltxr 7065 df-le 7066 df-icc 8764 |
This theorem is referenced by: iccshftri 8863 lincmb01cmp 8871 |
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