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Mirrors > Home > ILE Home > Th. List > 2rp | Unicode version |
Description: 2 is a positive real. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
2rp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2re 8783 | . 2 | |
2 | 2pos 8804 | . 2 | |
3 | 1, 2 | elrpii 9437 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 c2 8764 crp 9434 |
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 603 ax-in2 604 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-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 ax-setind 4447 ax-cnex 7704 ax-resscn 7705 ax-1cn 7706 ax-1re 7707 ax-icn 7708 ax-addcl 7709 ax-addrcl 7710 ax-mulcl 7711 ax-addcom 7713 ax-addass 7715 ax-i2m1 7718 ax-0lt1 7719 ax-0id 7721 ax-rnegex 7722 ax-pre-lttrn 7727 ax-pre-ltadd 7729 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ne 2307 df-nel 2402 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-xp 4540 df-iota 5083 df-fv 5126 df-ov 5770 df-pnf 7795 df-mnf 7796 df-ltxr 7798 df-2 8772 df-rp 9435 |
This theorem is referenced by: rphalfcl 9462 qbtwnrelemcalc 10026 flhalf 10068 cvg1nlemcxze 10747 cvg1nlemres 10750 resqrexlemdec 10776 resqrexlemlo 10778 resqrexlemcvg 10784 abstri 10869 maxabsle 10969 maxabslemlub 10972 maxltsup 10983 bdtri 11004 efcllemp 11353 cos12dec 11463 sin0pilem2 12852 cosordlem 12919 cvgcmp2nlemabs 13216 cvgcmp2n 13217 trilpolemclim 13218 trilpolemcl 13219 trilpolemisumle 13220 trilpolemeq1 13222 trilpolemlt1 13223 taupi 13228 |
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