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Mirrors > Home > ILE Home > Th. List > nn0re | Unicode version |
Description: A nonnegative integer is a real number. (Contributed by NM, 9-May-2004.) |
Ref | Expression |
---|---|
nn0re |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0ssre 9005 |
. 2
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2 | 1 | sseli 3098 |
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-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-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-cnex 7735 ax-resscn 7736 ax-1re 7738 ax-addrcl 7741 ax-rnegex 7753 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-int 3780 df-inn 8745 df-n0 9002 |
This theorem is referenced by: nn0nlt0 9027 nn0le0eq0 9029 nn0p1gt0 9030 elnnnn0c 9046 nn0addge1 9047 nn0addge2 9048 nn0ge2m1nn 9061 nn0nndivcl 9063 xnn0xr 9069 nn0nepnf 9072 xnn0nemnf 9075 elnn0z 9091 elznn0nn 9092 nn0lt10b 9155 nn0ge0div 9162 xnn0lenn0nn0 9678 xnn0xadd0 9680 nn0fz0 9930 elfz0fzfz0 9934 fz0fzelfz0 9935 fz0fzdiffz0 9938 fzctr 9941 difelfzle 9942 difelfznle 9943 elfzo0le 9993 fzonmapblen 9995 fzofzim 9996 elfzodifsumelfzo 10009 fzonn0p1 10019 fzonn0p1p1 10021 elfzom1p1elfzo 10022 ubmelm1fzo 10034 fvinim0ffz 10049 subfzo0 10050 adddivflid 10096 divfl0 10100 flltdivnn0lt 10108 addmodid 10176 modfzo0difsn 10199 inftonninf 10245 bernneq 10443 bernneq3 10445 facwordi 10518 faclbnd 10519 faclbnd3 10521 faclbnd6 10522 facubnd 10523 facavg 10524 bcval4 10530 bcval5 10541 bcpasc 10544 fihashneq0 10573 dvdseq 11582 oddge22np1 11614 nn0ehalf 11636 nn0o 11640 nn0oddm1d2 11642 gcdn0gt0 11702 nn0gcdid0 11705 absmulgcd 11741 nn0seqcvgd 11758 algcvgblem 11766 algcvga 11768 lcmgcdnn 11799 prmfac1 11866 nonsq 11921 hashgcdlem 11939 |
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