| Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > ILE Home > Th. List > 1rp | GIF version | ||
| Description: 1 is a positive real. (Contributed by Jeff Hankins, 23-Nov-2008.) |
| Ref | Expression |
|---|---|
| 1rp | ⊢ 1 ∈ ℝ+ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 1re 8071 | . 2 ⊢ 1 ∈ ℝ | |
| 2 | 0lt1 8199 | . 2 ⊢ 0 < 1 | |
| 3 | 1, 2 | elrpii 9778 | 1 ⊢ 1 ∈ ℝ+ |
| Colors of variables: wff set class |
| Syntax hints: ∈ wcel 2176 1c1 7926 ℝ+crp 9775 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 711 ax-5 1470 ax-7 1471 ax-gen 1472 ax-ie1 1516 ax-ie2 1517 ax-8 1527 ax-10 1528 ax-11 1529 ax-i12 1530 ax-bndl 1532 ax-4 1533 ax-17 1549 ax-i9 1553 ax-ial 1557 ax-i5r 1558 ax-13 2178 ax-14 2179 ax-ext 2187 ax-sep 4162 ax-pow 4218 ax-pr 4253 ax-un 4480 ax-setind 4585 ax-cnex 8016 ax-resscn 8017 ax-1re 8019 ax-addrcl 8022 ax-0lt1 8031 ax-rnegex 8034 |
| This theorem depends on definitions: df-bi 117 df-3an 983 df-tru 1376 df-fal 1379 df-nf 1484 df-sb 1786 df-eu 2057 df-mo 2058 df-clab 2192 df-cleq 2198 df-clel 2201 df-nfc 2337 df-ne 2377 df-nel 2472 df-ral 2489 df-rex 2490 df-rab 2493 df-v 2774 df-dif 3168 df-un 3170 df-in 3172 df-ss 3179 df-pw 3618 df-sn 3639 df-pr 3640 df-op 3642 df-uni 3851 df-br 4045 df-opab 4106 df-xp 4681 df-pnf 8109 df-mnf 8110 df-ltxr 8112 df-rp 9776 |
| This theorem is referenced by: rpreccl 9802 rpexpcl 10703 caubnd2 11428 climcaucn 11662 fprodrpcl 11922 isprm6 12469 unirnblps 14894 unirnbl 14895 mopnex 14977 tgioo 15026 cncfmptc 15068 dveflem 15198 log1 15338 logrpap0b 15348 rplogcl 15351 logge0 15352 logge0b 15362 loggt0b 15363 1cxp 15372 rplogb1 15420 logbrec 15432 logbgcd1irraplemexp 15440 iooref1o 15973 |
| Copyright terms: Public domain | W3C validator |