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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1nn 8845 | . 2 | |
2 | 1 | nnzi 9189 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2128 c1 7734 cz 9168 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 ax-un 4394 ax-setind 4497 ax-cnex 7824 ax-resscn 7825 ax-1cn 7826 ax-1re 7827 ax-icn 7828 ax-addcl 7829 ax-addrcl 7830 ax-mulcl 7831 ax-addcom 7833 ax-addass 7835 ax-distr 7837 ax-i2m1 7838 ax-0lt1 7839 ax-0id 7841 ax-rnegex 7842 ax-cnre 7844 ax-pre-ltirr 7845 ax-pre-ltwlin 7846 ax-pre-lttrn 7847 ax-pre-ltadd 7849 |
This theorem depends on definitions: df-bi 116 df-3or 964 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-nel 2423 df-ral 2440 df-rex 2441 df-reu 2442 df-rab 2444 df-v 2714 df-sbc 2938 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3774 df-int 3809 df-br 3967 df-opab 4027 df-id 4254 df-xp 4593 df-rel 4594 df-cnv 4595 df-co 4596 df-dm 4597 df-iota 5136 df-fun 5173 df-fv 5179 df-riota 5781 df-ov 5828 df-oprab 5829 df-mpo 5830 df-pnf 7915 df-mnf 7916 df-xr 7917 df-ltxr 7918 df-le 7919 df-sub 8049 df-neg 8050 df-inn 8835 df-z 9169 |
This theorem is referenced by: 1zzd 9195 znnnlt1 9216 nn0n0n1ge2b 9244 nn0lt2 9246 nn0le2is012 9247 3halfnz 9262 prime 9264 nnuz 9475 eluz2nn 9478 eluzge3nn 9484 1eluzge0 9486 2eluzge1 9488 eluz2b1 9513 uz2m1nn 9517 elnn1uz2 9519 nn01to3 9527 nnrecq 9555 fz1n 9947 fz10 9949 fz01en 9956 fzpreddisj 9974 fznatpl1 9979 fzprval 9985 fztpval 9986 fseq1p1m1 9997 elfzp1b 10000 elfzm1b 10001 4fvwrd4 10043 ige2m2fzo 10101 fzo12sn 10120 fzofzp1 10130 fzostep1 10140 rebtwn2zlemstep 10156 qbtwnxr 10161 flqge1nn 10197 fldiv4p1lem1div2 10208 modqfrac 10240 modqid0 10253 q1mod 10259 mulp1mod1 10268 m1modnnsub1 10273 modqm1p1mod0 10278 modqltm1p1mod 10279 frecfzennn 10329 frecfzen2 10330 zexpcl 10438 qexpcl 10439 qexpclz 10444 m1expcl 10446 expp1zap 10472 expm1ap 10473 bcn1 10636 bcpasc 10644 bcnm1 10650 isfinite4im 10671 hashsng 10676 hashfz 10699 climuni 11194 sum0 11289 sumsnf 11310 expcnv 11405 cvgratz 11433 prod0 11486 prodsnf 11493 sin01gt0 11662 p1modz1 11694 iddvds 11704 1dvds 11705 dvds1 11749 nn0o1gt2 11800 n2dvds1 11807 gcdadd 11873 gcdid 11874 gcd1 11875 1gcd 11880 bezoutlema 11887 bezoutlemb 11888 gcdmultiple 11908 lcmgcdlem 11958 lcm1 11962 3lcm2e6woprm 11967 isprm3 11999 prmgt1 12013 phicl2 12093 phibnd 12096 phi1 12098 dfphi2 12099 phimullem 12104 eulerthlemrprm 12108 eulerthlema 12109 eulerthlemth 12111 fermltl 12113 prmdiv 12114 prmdiveq 12115 odzcllem 12121 odzdvds 12124 oddprm 12138 pythagtriplem4 12147 ssnnctlemct 12217 sin2pim 13176 cos2pim 13177 rpcxp1 13262 logbleb 13320 logblt 13321 ex-fl 13343 apdiff 13661 iswomni0 13664 nconstwlpolem0 13675 |
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