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Mirrors > Home > ILE Home > Th. List > rpge0d | Unicode version |
Description: A positive real is greater than or equal to zero. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
rpred.1 |
Ref | Expression |
---|---|
rpge0d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpred.1 | . 2 | |
2 | rpge0 9574 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2128 class class class wbr 3966 cc0 7733 cle 7914 crp 9561 |
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 4083 ax-pow 4136 ax-pr 4170 ax-un 4394 ax-setind 4497 ax-cnex 7824 ax-resscn 7825 ax-1re 7827 ax-addrcl 7830 ax-rnegex 7842 ax-pre-ltirr 7845 ax-pre-lttrn 7847 |
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 3774 df-br 3967 df-opab 4027 df-xp 4593 df-cnv 4595 df-pnf 7915 df-mnf 7916 df-xr 7917 df-ltxr 7918 df-le 7919 df-rp 9562 |
This theorem is referenced by: rprege0d 9612 resqrexlemnm 10922 bdtrilem 11142 isumrpcl 11395 expcnvap0 11403 absgtap 11411 cvgratnnlemrate 11431 cvgratz 11433 ivthinclemlopn 13056 ivthinclemuopn 13058 limcimolemlt 13075 rpcxpsqrt 13284 rpabscxpbnd 13301 trilpolemclim 13649 trilpolemisumle 13651 trilpolemeq1 13653 trilpolemlt1 13654 nconstwlpolemgt0 13676 |
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