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Mirrors > Home > ILE Home > Th. List > uzssz | Unicode version |
Description: An upper set of integers is a subset of all integers. (Contributed by NM, 2-Sep-2005.) (Revised by Mario Carneiro, 3-Nov-2013.) |
Ref | Expression |
---|---|
uzssz |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluzelz 9328 | . 2 | |
2 | 1 | ssriv 3096 | 1 |
Colors of variables: wff set class |
Syntax hints: wss 3066 cfv 5118 cz 9047 cuz 9319 |
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-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-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-cnex 7704 ax-resscn 7705 |
This theorem depends on definitions: df-bi 116 df-3or 963 df-3an 964 df-tru 1334 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-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-sbc 2905 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-mpt 3986 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-res 4546 df-ima 4547 df-iota 5083 df-fun 5120 df-fn 5121 df-f 5122 df-fv 5126 df-ov 5770 df-neg 7929 df-z 9048 df-uz 9320 |
This theorem is referenced by: cau3 10880 climz 11054 serclim0 11067 climaddc1 11091 climmulc2 11093 climsubc1 11094 climsubc2 11095 climle 11096 climlec2 11103 summodclem2a 11143 summodclem2 11144 zsumdc 11146 fsum3cvg3 11158 iserabs 11237 isumshft 11252 explecnv 11267 clim2prod 11301 prodfclim1 11306 ntrivcvgap 11310 infssuzcldc 11633 exmidunben 11928 lmbrf 12373 lmres 12406 climcncf 12729 |
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