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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 108 | . . . . 5 | |
2 | readdcl 7871 | . . . . 5 | |
3 | 1, 2 | 2thd 174 | . . . 4 |
4 | 3 | adantl 275 | . . 3 |
5 | leadd1 8320 | . . . . . 6 | |
6 | 5 | 3expb 1193 | . . . . 5 |
7 | 6 | adantlr 469 | . . . 4 |
8 | iccshftr.1 | . . . . 5 | |
9 | 8 | breq1i 3984 | . . . 4 |
10 | 7, 9 | bitrdi 195 | . . 3 |
11 | leadd1 8320 | . . . . . . 7 | |
12 | 11 | 3expb 1193 | . . . . . 6 |
13 | 12 | an12s 555 | . . . . 5 |
14 | 13 | adantll 468 | . . . 4 |
15 | iccshftr.2 | . . . . 5 | |
16 | 15 | breq2i 3985 | . . . 4 |
17 | 14, 16 | bitrdi 195 | . . 3 |
18 | 4, 10, 17 | 3anbi123d 1301 | . 2 |
19 | elicc2 9866 | . . 3 | |
20 | 19 | adantr 274 | . 2 |
21 | readdcl 7871 | . . . . . 6 | |
22 | 8, 21 | eqeltrrid 2252 | . . . . 5 |
23 | readdcl 7871 | . . . . . 6 | |
24 | 15, 23 | eqeltrrid 2252 | . . . . 5 |
25 | elicc2 9866 | . . . . 5 | |
26 | 22, 24, 25 | syl2an 287 | . . . 4 |
27 | 26 | anandirs 583 | . . 3 |
28 | 27 | adantrl 470 | . 2 |
29 | 18, 20, 28 | 3bitr4d 219 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 967 wceq 1342 wcel 2135 class class class wbr 3977 (class class class)co 5837 cr 7744 caddc 7748 cle 7926 cicc 9819 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4095 ax-pow 4148 ax-pr 4182 ax-un 4406 ax-setind 4509 ax-cnex 7836 ax-resscn 7837 ax-1cn 7838 ax-icn 7840 ax-addcl 7841 ax-addrcl 7842 ax-mulcl 7843 ax-addcom 7845 ax-addass 7847 ax-i2m1 7850 ax-0id 7853 ax-rnegex 7854 ax-pre-ltirr 7857 ax-pre-ltwlin 7858 ax-pre-lttrn 7859 ax-pre-ltadd 7861 |
This theorem depends on definitions: df-bi 116 df-3or 968 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-nel 2430 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2724 df-sbc 2948 df-dif 3114 df-un 3116 df-in 3118 df-ss 3125 df-pw 3556 df-sn 3577 df-pr 3578 df-op 3580 df-uni 3785 df-br 3978 df-opab 4039 df-id 4266 df-po 4269 df-iso 4270 df-xp 4605 df-rel 4606 df-cnv 4607 df-co 4608 df-dm 4609 df-iota 5148 df-fun 5185 df-fv 5191 df-ov 5840 df-oprab 5841 df-mpo 5842 df-pnf 7927 df-mnf 7928 df-xr 7929 df-ltxr 7930 df-le 7931 df-icc 9823 |
This theorem is referenced by: iccshftri 9923 lincmb01cmp 9931 |
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