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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 8755 |
. 2
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2 | 1 | nnzi 9099 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-un 4363 ax-setind 4460 ax-cnex 7735 ax-resscn 7736 ax-1cn 7737 ax-1re 7738 ax-icn 7739 ax-addcl 7740 ax-addrcl 7741 ax-mulcl 7742 ax-addcom 7744 ax-addass 7746 ax-distr 7748 ax-i2m1 7749 ax-0lt1 7750 ax-0id 7752 ax-rnegex 7753 ax-cnre 7755 ax-pre-ltirr 7756 ax-pre-ltwlin 7757 ax-pre-lttrn 7758 ax-pre-ltadd 7760 |
This theorem depends on definitions: df-bi 116 df-3or 964 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ne 2310 df-nel 2405 df-ral 2422 df-rex 2423 df-reu 2424 df-rab 2426 df-v 2691 df-sbc 2914 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-int 3780 df-br 3938 df-opab 3998 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-iota 5096 df-fun 5133 df-fv 5139 df-riota 5738 df-ov 5785 df-oprab 5786 df-mpo 5787 df-pnf 7826 df-mnf 7827 df-xr 7828 df-ltxr 7829 df-le 7830 df-sub 7959 df-neg 7960 df-inn 8745 df-z 9079 |
This theorem is referenced by: 1zzd 9105 znnnlt1 9126 nn0n0n1ge2b 9154 nn0lt2 9156 nn0le2is012 9157 3halfnz 9172 prime 9174 nnuz 9385 eluz2nn 9388 eluzge3nn 9394 1eluzge0 9396 2eluzge1 9398 eluz2b1 9422 uz2m1nn 9426 elnn1uz2 9428 nn01to3 9436 nnrecq 9464 fz1n 9855 fz10 9857 fz01en 9864 fzpreddisj 9882 fznatpl1 9887 fzprval 9893 fztpval 9894 fseq1p1m1 9905 elfzp1b 9908 elfzm1b 9909 4fvwrd4 9948 ige2m2fzo 10006 fzo12sn 10025 fzofzp1 10035 fzostep1 10045 rebtwn2zlemstep 10061 qbtwnxr 10066 flqge1nn 10098 fldiv4p1lem1div2 10109 modqfrac 10141 modqid0 10154 q1mod 10160 mulp1mod1 10169 m1modnnsub1 10174 modqm1p1mod0 10179 modqltm1p1mod 10180 frecfzennn 10230 frecfzen2 10231 zexpcl 10339 qexpcl 10340 qexpclz 10345 m1expcl 10347 expp1zap 10373 expm1ap 10374 bcn1 10536 bcpasc 10544 bcnm1 10550 isfinite4im 10571 hashsng 10576 hashfz 10599 climuni 11094 sum0 11189 sumsnf 11210 expcnv 11305 cvgratz 11333 sin01gt0 11504 iddvds 11542 1dvds 11543 dvds1 11587 nn0o1gt2 11638 n2dvds1 11645 gcdadd 11709 gcdid 11710 gcd1 11711 1gcd 11716 bezoutlema 11723 bezoutlemb 11724 gcdmultiple 11744 lcmgcdlem 11794 lcm1 11798 3lcm2e6woprm 11803 isprm3 11835 prmgt1 11848 phicl2 11926 phibnd 11929 phi1 11931 dfphi2 11932 phimullem 11937 sin2pim 12942 cos2pim 12943 rpcxp1 13028 logbleb 13086 logblt 13087 ex-fl 13108 apdiff 13416 |
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