Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > fzval2 | Unicode version |
Description: An alternative way of expressing a finite set of sequential integers. (Contributed by Mario Carneiro, 3-Nov-2013.) |
Ref | Expression |
---|---|
fzval2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fzval 8876 | . 2 | |
2 | zssre 8252 | . . . . . . 7 | |
3 | ressxr 7069 | . . . . . . 7 | |
4 | 2, 3 | sstri 2954 | . . . . . 6 |
5 | 4 | sseli 2941 | . . . . 5 |
6 | 4 | sseli 2941 | . . . . 5 |
7 | iccval 8789 | . . . . 5 | |
8 | 5, 6, 7 | syl2an 273 | . . . 4 |
9 | 8 | ineq1d 3137 | . . 3 |
10 | inrab2 3210 | . . . 4 | |
11 | sseqin2 3156 | . . . . . 6 | |
12 | 4, 11 | mpbi 133 | . . . . 5 |
13 | rabeq 2551 | . . . . 5 | |
14 | 12, 13 | ax-mp 7 | . . . 4 |
15 | 10, 14 | eqtri 2060 | . . 3 |
16 | 9, 15 | syl6req 2089 | . 2 |
17 | 1, 16 | eqtrd 2072 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wceq 1243 wcel 1393 crab 2310 cin 2916 wss 2917 class class class wbr 3764 (class class class)co 5512 cr 6888 cxr 7059 cle 7061 cz 8245 cicc 8760 cfz 8874 |
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 |
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-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-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-neg 7185 df-z 8246 df-icc 8764 df-fz 8875 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |