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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 8629 | . 2 | |
2 | 1 | recnd 7147 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1433 cfv 4922 cc 6979 cuz 8619 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 ax-cnex 7067 ax-resscn 7068 |
This theorem depends on definitions: df-bi 115 df-3or 920 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-rab 2357 df-v 2603 df-sbc 2816 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-mpt 3841 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-res 4375 df-ima 4376 df-iota 4887 df-fun 4924 df-fn 4925 df-f 4926 df-fv 4930 df-ov 5535 df-neg 7282 df-z 8352 df-uz 8620 |
This theorem is referenced by: uzp1 8652 peano2uzr 8673 uzaddcl 8674 eluzgtdifelfzo 9206 rebtwn2zlemstep 9261 mulp1mod1 9367 iseqm1 9447 facnn 9654 fac0 9655 fac1 9656 facp1 9657 ibcval5 9690 bcn2 9691 shftuz 9705 climshftlemg 10141 climshft 10143 dvdsexp 10261 |
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