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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 7877 | . 2 ⊢ 1 ∈ ℝ | |
2 | 0lt1 8002 | . 2 ⊢ 0 < 1 | |
3 | 1, 2 | elrpii 9563 | 1 ⊢ 1 ∈ ℝ+ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2128 1c1 7733 ℝ+crp 9560 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 ax-un 4393 ax-setind 4496 ax-cnex 7823 ax-resscn 7824 ax-1re 7826 ax-addrcl 7829 ax-0lt1 7838 ax-rnegex 7841 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-nel 2423 df-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-opab 4026 df-xp 4592 df-pnf 7914 df-mnf 7915 df-ltxr 7917 df-rp 9561 |
This theorem is referenced by: rpreccl 9587 rpexpcl 10438 caubnd2 11017 climcaucn 11248 fprodrpcl 11508 isprm6 12022 unirnblps 12833 unirnbl 12834 mopnex 12916 tgioo 12957 cncfmptc 12993 dveflem 13098 log1 13198 logrpap0b 13208 rplogcl 13211 logge0 13212 logge0b 13222 loggt0b 13223 1cxp 13232 rplogb1 13276 logbrec 13288 logbgcd1irraplemexp 13296 iooref1o 13616 |
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