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Mirrors > Home > ILE Home > Th. List > fzval2 | Unicode version |
Description: An alternate 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 9823 | . 2 | |
2 | zssre 9085 | . . . . . . 7 | |
3 | ressxr 7833 | . . . . . . 7 | |
4 | 2, 3 | sstri 3111 | . . . . . 6 |
5 | 4 | sseli 3098 | . . . . 5 |
6 | 4 | sseli 3098 | . . . . 5 |
7 | iccval 9733 | . . . . 5 | |
8 | 5, 6, 7 | syl2an 287 | . . . 4 |
9 | 8 | ineq1d 3281 | . . 3 |
10 | inrab2 3354 | . . . 4 | |
11 | sseqin2 3300 | . . . . . 6 | |
12 | 4, 11 | mpbi 144 | . . . . 5 |
13 | rabeq 2681 | . . . . 5 | |
14 | 12, 13 | ax-mp 5 | . . . 4 |
15 | 10, 14 | eqtri 2161 | . . 3 |
16 | 9, 15 | eqtr2di 2190 | . 2 |
17 | 1, 16 | eqtrd 2173 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1332 wcel 1481 crab 2421 cin 3075 wss 3076 class class class wbr 3937 (class class class)co 5782 cr 7643 cxr 7823 cle 7825 cz 9078 cicc 9704 cfz 9821 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-un 4363 ax-setind 4460 ax-cnex 7735 ax-resscn 7736 |
This theorem depends on definitions: df-bi 116 df-3or 964 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ne 2310 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-sbc 2914 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-iota 5096 df-fun 5133 df-fv 5139 df-ov 5785 df-oprab 5786 df-mpo 5787 df-pnf 7826 df-mnf 7827 df-xr 7828 df-neg 7960 df-z 9079 df-icc 9708 df-fz 9822 |
This theorem is referenced by: (None) |
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