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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 8918 | . 2 | |
2 | 2pos 8939 | . 2 | |
3 | 1, 2 | elrpii 9583 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2135 c2 8899 crp 9580 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-un 4405 ax-setind 4508 ax-cnex 7835 ax-resscn 7836 ax-1cn 7837 ax-1re 7838 ax-icn 7839 ax-addcl 7840 ax-addrcl 7841 ax-mulcl 7842 ax-addcom 7844 ax-addass 7846 ax-i2m1 7849 ax-0lt1 7850 ax-0id 7852 ax-rnegex 7853 ax-pre-lttrn 7858 ax-pre-ltadd 7860 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-nel 2430 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2723 df-dif 3113 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-xp 4604 df-iota 5147 df-fv 5190 df-ov 5839 df-pnf 7926 df-mnf 7927 df-ltxr 7929 df-2 8907 df-rp 9581 |
This theorem is referenced by: rphalfcl 9608 qbtwnrelemcalc 10181 flhalf 10227 cvg1nlemcxze 10910 cvg1nlemres 10913 resqrexlemdec 10939 resqrexlemlo 10941 resqrexlemcvg 10947 abstri 11032 maxabsle 11132 maxabslemlub 11135 maxltsup 11146 bdtri 11167 efcllemp 11585 cos12dec 11694 oddprm 12170 sin0pilem2 13250 cosordlem 13317 2logb9irrALT 13439 sqrt2cxp2logb9e3 13440 cvgcmp2nlemabs 13752 cvgcmp2n 13753 trilpolemclim 13756 trilpolemcl 13757 trilpolemisumle 13758 trilpolemeq1 13760 trilpolemlt1 13761 apdifflemf 13766 nconstwlpolemgt0 13783 taupi 13790 |
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