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Mirrors > Home > ILE Home > Th. List > eluzelcn | Unicode version |
Description: A member of an upper set of integers is a complex number. (Contributed by Glauco Siliprandi, 29-Jun-2017.) |
Ref | Expression |
---|---|
eluzelcn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluzelre 9304 | . 2 | |
2 | 1 | recnd 7762 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1465 cfv 5093 cc 7586 cuz 9294 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-cnex 7679 ax-resscn 7680 |
This theorem depends on definitions: df-bi 116 df-3or 948 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 df-iota 5058 df-fun 5095 df-fn 5096 df-f 5097 df-fv 5101 df-ov 5745 df-neg 7904 df-z 9023 df-uz 9295 |
This theorem is referenced by: uzp1 9327 peano2uzr 9348 uzaddcl 9349 eluzgtdifelfzo 9942 rebtwn2zlemstep 9998 mulp1mod1 10106 seq3m1 10209 facnn 10441 fac0 10442 fac1 10443 facp1 10444 bcval5 10477 bcn2 10478 shftuz 10557 seq3shft 10578 climshftlemg 11039 climshft 11041 isumshft 11227 dvdsexp 11486 |
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