![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 1rp | Unicode version |
Description: 1 is a positive real. (Contributed by Jeff Hankins, 23-Nov-2008.) |
Ref | Expression |
---|---|
1rp |
![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1re 7789 |
. 2
![]() ![]() ![]() ![]() | |
2 | 0lt1 7913 |
. 2
![]() ![]() ![]() ![]() | |
3 | 1, 2 | elrpii 9473 |
1
![]() ![]() ![]() ![]() |
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-in1 604 ax-in2 605 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-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-un 4363 ax-setind 4460 ax-cnex 7735 ax-resscn 7736 ax-1re 7738 ax-addrcl 7741 ax-0lt1 7750 ax-rnegex 7753 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ne 2310 df-nel 2405 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-xp 4553 df-pnf 7826 df-mnf 7827 df-ltxr 7829 df-rp 9471 |
This theorem is referenced by: rpreccl 9497 rpexpcl 10343 caubnd2 10921 climcaucn 11152 isprm6 11861 unirnblps 12630 unirnbl 12631 mopnex 12713 tgioo 12754 cncfmptc 12790 dveflem 12895 log1 12995 logrpap0b 13005 rplogcl 13008 logge0 13009 logge0b 13019 loggt0b 13020 1cxp 13029 rplogb1 13073 logbrec 13085 logbgcd1irraplemexp 13093 iooref1o 13426 |
Copyright terms: Public domain | W3C validator |