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Mirrors > Home > ILE Home > Th. List > elnnuz | Unicode version |
Description: A positive integer expressed as a member of an upper set of integers. (Contributed by NM, 6-Jun-2006.) |
Ref | Expression |
---|---|
elnnuz |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnuz 9561 |
. 2
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2 | 1 | eleq2i 2244 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-pow 4174 ax-pr 4209 ax-un 4433 ax-setind 4536 ax-cnex 7901 ax-resscn 7902 ax-1cn 7903 ax-1re 7904 ax-icn 7905 ax-addcl 7906 ax-addrcl 7907 ax-mulcl 7908 ax-addcom 7910 ax-addass 7912 ax-distr 7914 ax-i2m1 7915 ax-0lt1 7916 ax-0id 7918 ax-rnegex 7919 ax-cnre 7921 ax-pre-ltirr 7922 ax-pre-ltwlin 7923 ax-pre-lttrn 7924 ax-pre-ltadd 7926 |
This theorem depends on definitions: df-bi 117 df-3or 979 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-nel 2443 df-ral 2460 df-rex 2461 df-reu 2462 df-rab 2464 df-v 2739 df-sbc 2963 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-int 3845 df-br 4004 df-opab 4065 df-mpt 4066 df-id 4293 df-xp 4632 df-rel 4633 df-cnv 4634 df-co 4635 df-dm 4636 df-iota 5178 df-fun 5218 df-fv 5224 df-riota 5830 df-ov 5877 df-oprab 5878 df-mpo 5879 df-pnf 7992 df-mnf 7993 df-xr 7994 df-ltxr 7995 df-le 7996 df-sub 8128 df-neg 8129 df-inn 8918 df-z 9252 df-uz 9527 |
This theorem is referenced by: eluzge3nn 9570 uznnssnn 9575 elnndc 9610 uzsubsubfz1 10045 elfz1end 10052 fznn 10086 fzo1fzo0n0 10180 elfzonlteqm1 10207 rebtwn2z 10252 nnsinds 10440 exp3vallem 10518 exp1 10523 expp1 10524 facp1 10705 faclbnd 10716 bcn1 10733 resqrexlemf1 11012 resqrexlemfp1 11013 summodclem3 11383 summodclem2a 11384 fsum3 11390 fsumcl2lem 11401 fsumadd 11409 sumsnf 11412 fsummulc2 11451 trireciplem 11503 geo2lim 11519 geoisum1 11522 geoisum1c 11523 cvgratnnlemnexp 11527 cvgratz 11535 prodmodclem3 11578 prodmodclem2a 11579 fprodseq 11586 fprodmul 11594 prodsnf 11595 fprodfac 11618 dvdsfac 11860 gcdsupex 11952 gcdsupcl 11953 prmind2 12114 eulerthlemrprm 12223 eulerthlema 12224 pcmpt 12335 prmunb 12354 nninfdclemp1 12445 structfn 12475 mulg1 12944 mulgnndir 12965 lgsval2lem 14304 lgsdir 14329 lgsdilem2 14330 lgsdi 14331 lgsne0 14332 2sqlem10 14354 cvgcmp2nlemabs 14662 trilpolemisumle 14668 nconstwlpolem0 14692 |
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