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Mirrors > Home > ILE Home > Th. List > nnre | Unicode version |
Description: A positive integer is a real number. (Contributed by NM, 18-Aug-1999.) |
Ref | Expression |
---|---|
nnre |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnssre 8748 | . 2 | |
2 | 1 | sseli 3098 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1481 cr 7643 cn 8744 |
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 |
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-v 2691 df-in 3082 df-ss 3089 df-int 3780 df-inn 8745 |
This theorem is referenced by: nnrei 8753 peano2nn 8756 nn1suc 8763 nnge1 8767 nnle1eq1 8768 nngt0 8769 nnnlt1 8770 nnap0 8773 nn2ge 8777 nn1gt1 8778 nndivre 8780 nnrecgt0 8782 nnsub 8783 arch 8998 nnrecl 8999 bndndx 9000 nn0ge0 9026 0mnnnnn0 9033 nnnegz 9081 elnnz 9088 elz2 9146 gtndiv 9170 prime 9174 btwnz 9194 qre 9444 elpq 9467 elpqb 9468 nnrp 9480 nnledivrp 9583 fzo1fzo0n0 9991 elfzo0le 9993 fzonmapblen 9995 ubmelfzo 10008 fzonn0p1p1 10021 elfzom1p1elfzo 10022 ubmelm1fzo 10034 subfzo0 10050 adddivflid 10096 flltdivnn0lt 10108 intfracq 10124 flqdiv 10125 m1modnnsub1 10174 addmodid 10176 modfzo0difsn 10199 nnlesq 10427 facndiv 10517 faclbnd 10519 faclbnd3 10521 bcval5 10541 seq3coll 10617 caucvgre 10785 efaddlem 11417 nndivdvds 11535 nno 11639 nnoddm1d2 11643 divalglemnn 11651 divalg2 11659 ndvdsadd 11664 gcdmultiple 11744 gcdmultiplez 11745 gcdzeq 11746 sqgcd 11753 dvdssqlem 11754 lcmgcdlem 11794 coprmgcdb 11805 qredeq 11813 qredeu 11814 prmdvdsfz 11855 sqrt2irr 11876 divdenle 11911 phibndlem 11928 hashgcdlem 11939 oddennn 11941 exmidunben 11975 |
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