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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 |
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Ref | Expression |
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rpge0d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpred.1 |
. 2
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2 | rpge0 9684 |
. 2
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3 | 1, 2 | syl 14 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4189 ax-pr 4224 ax-un 4448 ax-setind 4551 ax-cnex 7920 ax-resscn 7921 ax-1re 7923 ax-addrcl 7926 ax-rnegex 7938 ax-pre-ltirr 7941 ax-pre-lttrn 7943 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-nel 2456 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-xp 4647 df-cnv 4649 df-pnf 8012 df-mnf 8013 df-xr 8014 df-ltxr 8015 df-le 8016 df-rp 9672 |
This theorem is referenced by: rprege0d 9722 resqrexlemnm 11045 bdtrilem 11265 isumrpcl 11520 expcnvap0 11528 absgtap 11536 cvgratnnlemrate 11556 cvgratz 11558 4sqlem7 12400 ivthinclemlopn 14498 ivthinclemuopn 14500 limcimolemlt 14517 rpcxpsqrt 14726 rpabscxpbnd 14743 trilpolemclim 15169 trilpolemisumle 15171 trilpolemeq1 15173 trilpolemlt1 15174 nconstwlpolemgt0 15197 |
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