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Mirrors > Home > ILE Home > Th. List > 1z | Unicode version |
Description: One is an integer. (Contributed by NM, 10-May-2004.) |
Ref | Expression |
---|---|
1z |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1nn 8928 |
. 2
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2 | 1 | nnzi 9272 |
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-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 |
This theorem is referenced by: 1zzd 9278 znnnlt1 9299 nn0n0n1ge2b 9330 nn0lt2 9332 nn0le2is012 9333 3halfnz 9348 prime 9350 nnuz 9561 eluz2nn 9564 eluzge3nn 9570 1eluzge0 9572 2eluzge1 9574 eluz2b1 9599 uz2m1nn 9603 elnn1uz2 9605 elnndc 9610 nn01to3 9615 nnrecq 9643 fz1n 10041 fz10 10043 fz01en 10050 fzpreddisj 10068 fznatpl1 10073 fzprval 10079 fztpval 10080 fseq1p1m1 10091 elfzp1b 10094 elfzm1b 10095 4fvwrd4 10137 ige2m2fzo 10195 fzo12sn 10214 fzofzp1 10224 fzostep1 10234 rebtwn2zlemstep 10250 qbtwnxr 10255 flqge1nn 10291 fldiv4p1lem1div2 10302 modqfrac 10334 modqid0 10347 q1mod 10353 mulp1mod1 10362 m1modnnsub1 10367 modqm1p1mod0 10372 modqltm1p1mod 10373 frecfzennn 10423 frecfzen2 10424 zexpcl 10532 qexpcl 10533 qexpclz 10538 m1expcl 10540 expp1zap 10566 expm1ap 10567 bcn1 10733 bcpasc 10741 bcnm1 10747 isfinite4im 10767 hashsng 10773 hashfz 10796 climuni 11296 sum0 11391 sumsnf 11412 expcnv 11507 cvgratz 11535 prod0 11588 prodsnf 11595 sin01gt0 11764 p1modz1 11796 iddvds 11806 1dvds 11807 dvds1 11853 nn0o1gt2 11904 n2dvds1 11911 gcdadd 11980 gcdid 11981 gcd1 11982 1gcd 11987 bezoutlema 11994 bezoutlemb 11995 gcdmultiple 12015 lcmgcdlem 12071 lcm1 12075 3lcm2e6woprm 12080 isprm3 12112 prmgt1 12126 phicl2 12208 phibnd 12211 phi1 12213 dfphi2 12214 phimullem 12219 eulerthlemrprm 12223 eulerthlema 12224 eulerthlemth 12226 fermltl 12228 prmdiv 12229 prmdiveq 12230 odzcllem 12236 odzdvds 12239 oddprm 12253 pythagtriplem4 12262 pcpre1 12286 pc1 12299 pcrec 12302 pcmpt 12335 fldivp1 12340 expnprm 12345 pockthlem 12348 igz 12366 ssnnctlemct 12441 mulgm1 12957 mulgp1 12969 mulgneg2 12970 zsubrg 13366 gzsubrg 13367 zringmulg 13379 sin2pim 14127 cos2pim 14128 rpcxp1 14213 logbleb 14272 logblt 14273 lgslem2 14295 lgsfcl2 14300 lgsval2lem 14304 lgsmod 14320 lgsdir2lem1 14322 lgsdir2lem5 14326 lgsdir 14329 lgsne0 14332 1lgs 14337 lgsdinn0 14342 2sqlem9 14353 2sqlem10 14354 ex-fl 14359 apdiff 14678 iswomni0 14681 nconstwlpolem0 14692 |
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