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Mirrors > Home > ILE Home > Th. List > 2rp | GIF version |
Description: 2 is a positive real. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
2rp | ⊢ 2 ∈ ℝ+ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2re 8758 | . 2 ⊢ 2 ∈ ℝ | |
2 | 2pos 8779 | . 2 ⊢ 0 < 2 | |
3 | 1, 2 | elrpii 9412 | 1 ⊢ 2 ∈ ℝ+ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1465 2c2 8739 ℝ+crp 9409 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-un 4325 ax-setind 4422 ax-cnex 7679 ax-resscn 7680 ax-1cn 7681 ax-1re 7682 ax-icn 7683 ax-addcl 7684 ax-addrcl 7685 ax-mulcl 7686 ax-addcom 7688 ax-addass 7690 ax-i2m1 7693 ax-0lt1 7694 ax-0id 7696 ax-rnegex 7697 ax-pre-lttrn 7702 ax-pre-ltadd 7704 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-nel 2381 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-xp 4515 df-iota 5058 df-fv 5101 df-ov 5745 df-pnf 7770 df-mnf 7771 df-ltxr 7773 df-2 8747 df-rp 9410 |
This theorem is referenced by: rphalfcl 9437 qbtwnrelemcalc 10001 flhalf 10043 cvg1nlemcxze 10722 cvg1nlemres 10725 resqrexlemdec 10751 resqrexlemlo 10753 resqrexlemcvg 10759 abstri 10844 maxabsle 10944 maxabslemlub 10947 maxltsup 10958 bdtri 10979 efcllemp 11291 cos12dec 11401 sin0pilem2 12790 cosordlem 12857 cvgcmp2nlemabs 13154 cvgcmp2n 13155 trilpolemclim 13156 trilpolemcl 13157 trilpolemisumle 13158 trilpolemeq1 13160 trilpolemlt1 13161 taupi 13166 |
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