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Mirrors > Home > ILE Home > Th. List > fzval | Unicode version |
Description: The value of a finite set of sequential integers. E.g., means the set . A special case of this definition (starting at 1) appears as Definition 11-2.1 of [Gleason] p. 141, where k means our ; he calls these sets segments of the integers. (Contributed by NM, 6-Sep-2005.) (Revised by Mario Carneiro, 3-Nov-2013.) |
Ref | Expression |
---|---|
fzval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq1 3968 | . . . 4 | |
2 | 1 | anbi1d 461 | . . 3 |
3 | 2 | rabbidv 2701 | . 2 |
4 | breq2 3969 | . . . 4 | |
5 | 4 | anbi2d 460 | . . 3 |
6 | 5 | rabbidv 2701 | . 2 |
7 | df-fz 9908 | . 2 | |
8 | zex 9171 | . . 3 | |
9 | 8 | rabex 4108 | . 2 |
10 | 3, 6, 7, 9 | ovmpo 5953 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wcel 2128 crab 2439 class class class wbr 3965 (class class class)co 5821 cle 7908 cz 9162 cfz 9907 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 ax-setind 4495 ax-cnex 7818 ax-resscn 7819 |
This theorem depends on definitions: df-bi 116 df-3or 964 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-sbc 2938 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-opab 4026 df-id 4253 df-xp 4591 df-rel 4592 df-cnv 4593 df-co 4594 df-dm 4595 df-iota 5134 df-fun 5171 df-fv 5177 df-ov 5824 df-oprab 5825 df-mpo 5826 df-neg 8044 df-z 9163 df-fz 9908 |
This theorem is referenced by: fzval2 9910 elfz1 9912 fznlem 9938 |
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