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Mirrors > Home > MPE Home > Th. List > nnrei | Structured version Visualization version Unicode version |
Description: A positive integer is a real number. (Contributed by NM, 18-Aug-1999.) |
Ref | Expression |
---|---|
nnre.1 |
Ref | Expression |
---|---|
nnrei |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnre.1 | . 2 | |
2 | nnre 11027 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wcel 1990 cr 9935 cn 11020 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-addrcl 9997 ax-mulcl 9998 ax-mulrcl 9999 ax-i2m1 10004 ax-1ne0 10005 ax-rrecex 10008 ax-cnre 10009 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-pss 3590 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-tp 4182 df-op 4184 df-uni 4437 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-tr 4753 df-id 5024 df-eprel 5029 df-po 5035 df-so 5036 df-fr 5073 df-we 5075 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-pred 5680 df-ord 5726 df-on 5727 df-lim 5728 df-suc 5729 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-ov 6653 df-om 7066 df-wrecs 7407 df-recs 7468 df-rdg 7506 df-nn 11021 |
This theorem is referenced by: nncni 11030 nnne0i 11055 10re 11517 numlt 11527 numltc 11528 faclbnd4lem1 13080 ef01bndlem 14914 dvdslelem 15031 divalglem6 15121 pockthi 15611 modsubi 15776 prmlem1 15814 prmlem2 15827 strlemor1OLD 15969 strleun 15972 strle1 15973 oppchomfval 16374 oppcbas 16378 rescco 16492 opprlem 18628 sralem 19177 opsrbaslem 19477 opsrbaslemOLD 19478 zlmlem 19865 znbaslem 19886 znbaslemOLD 19887 tnglem 22444 log2ublem1 24673 log2ublem2 24674 log2ub 24676 bpos1lem 25007 bposlem8 25016 bposlem9 25017 ttgval 25755 ttglem 25756 cchhllem 25767 slotsbaseefdif 25873 structvtxvallem 25909 lmat22e12 29885 lmat22e21 29886 lmat22e22 29887 ballotlem2 30550 ballotlem5 30561 ballotth 30599 chtvalz 30707 hgt750lem 30729 tgoldbachgt 30741 cnndvlem1 32528 hlhilslem 37230 jm2.27dlem2 37577 bgoldbtbndlem1 41693 tgblthelfgott 41703 tgoldbachlt 41704 tgblthelfgottOLD 41709 tgoldbachltOLD 41710 |
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