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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 8731 | . 2 | |
2 | 1 | nnzi 9075 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 c1 7621 cz 9054 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 ax-setind 4452 ax-cnex 7711 ax-resscn 7712 ax-1cn 7713 ax-1re 7714 ax-icn 7715 ax-addcl 7716 ax-addrcl 7717 ax-mulcl 7718 ax-addcom 7720 ax-addass 7722 ax-distr 7724 ax-i2m1 7725 ax-0lt1 7726 ax-0id 7728 ax-rnegex 7729 ax-cnre 7731 ax-pre-ltirr 7732 ax-pre-ltwlin 7733 ax-pre-lttrn 7734 ax-pre-ltadd 7736 |
This theorem depends on definitions: df-bi 116 df-3or 963 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-nel 2404 df-ral 2421 df-rex 2422 df-reu 2423 df-rab 2425 df-v 2688 df-sbc 2910 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-int 3772 df-br 3930 df-opab 3990 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-iota 5088 df-fun 5125 df-fv 5131 df-riota 5730 df-ov 5777 df-oprab 5778 df-mpo 5779 df-pnf 7802 df-mnf 7803 df-xr 7804 df-ltxr 7805 df-le 7806 df-sub 7935 df-neg 7936 df-inn 8721 df-z 9055 |
This theorem is referenced by: 1zzd 9081 znnnlt1 9102 nn0n0n1ge2b 9130 nn0lt2 9132 nn0le2is012 9133 3halfnz 9148 prime 9150 nnuz 9361 eluz2nn 9364 eluzge3nn 9367 1eluzge0 9369 2eluzge1 9371 eluz2b1 9395 uz2m1nn 9399 elnn1uz2 9401 nn01to3 9409 nnrecq 9437 fz1n 9824 fz10 9826 fz01en 9833 fzpreddisj 9851 fznatpl1 9856 fzprval 9862 fztpval 9863 fseq1p1m1 9874 elfzp1b 9877 elfzm1b 9878 4fvwrd4 9917 ige2m2fzo 9975 fzo12sn 9994 fzofzp1 10004 fzostep1 10014 rebtwn2zlemstep 10030 qbtwnxr 10035 flqge1nn 10067 fldiv4p1lem1div2 10078 modqfrac 10110 modqid0 10123 q1mod 10129 mulp1mod1 10138 m1modnnsub1 10143 modqm1p1mod0 10148 modqltm1p1mod 10149 frecfzennn 10199 frecfzen2 10200 zexpcl 10308 qexpcl 10309 qexpclz 10314 m1expcl 10316 expp1zap 10342 expm1ap 10343 bcn1 10504 bcpasc 10512 bcnm1 10518 isfinite4im 10539 hashsng 10544 hashfz 10567 climuni 11062 sum0 11157 sumsnf 11178 expcnv 11273 cvgratz 11301 sin01gt0 11468 iddvds 11506 1dvds 11507 dvds1 11551 nn0o1gt2 11602 n2dvds1 11609 gcdadd 11673 gcdid 11674 gcd1 11675 1gcd 11680 bezoutlema 11687 bezoutlemb 11688 gcdmultiple 11708 lcmgcdlem 11758 lcm1 11762 3lcm2e6woprm 11767 isprm3 11799 prmgt1 11812 phicl2 11890 phibnd 11893 phi1 11895 dfphi2 11896 phimullem 11901 sin2pim 12894 cos2pim 12895 ex-fl 12937 |
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