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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 9785 | . 2 | |
2 | zssre 9054 | . . . . . . 7 | |
3 | ressxr 7802 | . . . . . . 7 | |
4 | 2, 3 | sstri 3101 | . . . . . 6 |
5 | 4 | sseli 3088 | . . . . 5 |
6 | 4 | sseli 3088 | . . . . 5 |
7 | iccval 9696 | . . . . 5 | |
8 | 5, 6, 7 | syl2an 287 | . . . 4 |
9 | 8 | ineq1d 3271 | . . 3 |
10 | inrab2 3344 | . . . 4 | |
11 | sseqin2 3290 | . . . . . 6 | |
12 | 4, 11 | mpbi 144 | . . . . 5 |
13 | rabeq 2673 | . . . . 5 | |
14 | 12, 13 | ax-mp 5 | . . . 4 |
15 | 10, 14 | eqtri 2158 | . . 3 |
16 | 9, 15 | syl6req 2187 | . 2 |
17 | 1, 16 | eqtrd 2170 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 crab 2418 cin 3065 wss 3066 class class class wbr 3924 (class class class)co 5767 cr 7612 cxr 7792 cle 7794 cz 9047 cicc 9667 cfz 9783 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 ax-setind 4447 ax-cnex 7704 ax-resscn 7705 |
This theorem depends on definitions: df-bi 116 df-3or 963 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ne 2307 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-sbc 2905 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-iota 5083 df-fun 5120 df-fv 5126 df-ov 5770 df-oprab 5771 df-mpo 5772 df-pnf 7795 df-mnf 7796 df-xr 7797 df-neg 7929 df-z 9048 df-icc 9671 df-fz 9784 |
This theorem is referenced by: (None) |
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