Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nnred | Unicode version |
Description: A positive integer is a real number. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
nnred.1 |
Ref | Expression |
---|---|
nnred |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnssre 8717 | . 2 | |
2 | nnred.1 | . 2 | |
3 | 1, 2 | sseldi 3090 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 cr 7612 cn 8713 |
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 |
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-v 2683 df-in 3072 df-ss 3079 df-int 3767 df-inn 8714 |
This theorem is referenced by: exbtwnzlemstep 10018 qbtwnrelemcalc 10026 qbtwnre 10027 flqdiv 10087 modqmulnn 10108 modifeq2int 10152 modaddmodup 10153 modaddmodlo 10154 modsumfzodifsn 10162 addmodlteq 10164 bernneq3 10407 expnbnd 10408 facwordi 10479 faclbnd 10480 faclbnd2 10481 faclbnd3 10482 faclbnd6 10483 facubnd 10484 facavg 10485 bcp1nk 10501 bcval5 10502 caucvgrelemcau 10745 caucvgre 10746 cvg1nlemcxze 10747 cvg1nlemcau 10749 cvg1nlemres 10750 resqrexlemdecn 10777 resqrexlemga 10788 fsum3cvg3 11158 divcnv 11259 cvgratnnlembern 11285 cvgratnnlemseq 11288 cvgratnnlemabsle 11289 cvgratnnlemsumlt 11290 cvgratnnlemrate 11292 cvgratz 11294 eftabs 11351 efcllemp 11353 ege2le3 11366 efcj 11368 eftlub 11385 eflegeo 11397 eirraplem 11472 dvdslelemd 11530 nno 11592 nnoddm1d2 11596 divalglemnqt 11606 divalglemeunn 11607 dvdsbnd 11634 sqgcd 11706 lcmgcdlem 11747 ncoprmgcdne1b 11759 prmind2 11790 coprm 11811 prmfac1 11819 sqrt2irraplemnn 11846 divdenle 11864 qnumgt0 11865 nn0sqrtelqelz 11873 hashdvds 11886 znnen 11900 exmidunben 11928 strleund 12036 cvgcmp2nlemabs 13216 |
Copyright terms: Public domain | W3C validator |