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Mirrors > Home > ILE Home > Th. List > nn0red | Unicode version |
Description: A nonnegative integer is a real number. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
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nn0red.1 |
Ref | Expression |
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nn0red |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0ssre 8974 | . 2 | |
2 | nn0red.1 | . 2 | |
3 | 1, 2 | sseldi 3090 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 cr 7612 cn0 8970 |
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 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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-cnex 7704 ax-resscn 7705 ax-1re 7707 ax-addrcl 7710 ax-rnegex 7722 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-sn 3528 df-int 3767 df-inn 8714 df-n0 8971 |
This theorem is referenced by: nn0cnd 9025 nn0readdcl 9029 nn01to3 9402 flqmulnn0 10065 modifeq2int 10152 modaddmodup 10153 modaddmodlo 10154 modsumfzodifsn 10162 expnegap0 10294 nn0le2msqd 10458 nn0opthlem2d 10460 nn0opthd 10461 faclbnd6 10483 bcval5 10502 filtinf 10531 zfz1isolemiso 10575 mertenslemi1 11297 efcllemp 11353 eftlub 11385 oddge22np1 11567 nn0oddm1d2 11595 gcdaddm 11661 bezoutlemsup 11686 gcdzeq 11699 dvdssqlem 11707 nn0seqcvgd 11711 lcmneg 11744 mulgcddvds 11764 qredeu 11767 pw2dvdseulemle 11834 pw2dvdseu 11835 nn0sqrtelqelz 11873 nonsq 11874 ennnfoneleminc 11913 ennnfonelemkh 11914 ennnfonelemex 11916 ennnfonelemim 11926 |
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