Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > eluzelcn | Structured version Visualization version 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 11698 | . 2 | |
2 | 1 | recnd 10068 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 cfv 5888 cc 9934 cuz 11687 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-cnex 9992 ax-resscn 9993 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-fv 5896 df-ov 6653 df-neg 10269 df-z 11378 df-uz 11688 |
This theorem is referenced by: uzp1 11721 peano2uzr 11743 uzaddcl 11744 eluzgtdifelfzo 12529 fzosplitpr 12577 fldiv4lem1div2uz2 12637 mulp1mod1 12711 seqm1 12818 bcval5 13105 swrdfv2 13446 relexpaddg 13793 shftuz 13809 seqshft 13825 climshftlem 14305 climshft 14307 isumshft 14571 dvdsexp 15049 pclem 15543 efgtlen 18139 dvradcnv 24175 clwwlksext2edg 26923 extwwlkfablem1 27207 numclwwlkovf2exlem1 27211 numclwwlkovf2exlem2 27212 numclwwlkovf2ex 27219 numclwlk1lem2foalem 27222 numclwlk1lem2fo 27228 numclwwlk2 27240 nn0prpwlem 32317 rmspecsqrtnq 37470 rmspecsqrtnqOLD 37471 rmxm1 37499 rmym1 37500 rmxluc 37501 rmyluc 37502 rmyluc2 37503 jm2.17a 37527 relexpaddss 38010 trclfvdecomr 38020 binomcxplemnn0 38548 stoweidlem14 40231 fmtnorec3 41460 lighneallem4a 41525 lighneallem4b 41526 evengpop3 41686 evengpoap3 41687 nnsum4primeseven 41688 nnsum4primesevenALTV 41689 expnegico01 42308 dignn0ldlem 42396 dignnld 42397 digexp 42401 dig1 42402 nn0sumshdiglemB 42414 |
Copyright terms: Public domain | W3C validator |