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Mirrors > Home > ILE Home > Th. List > rpgt0d | Unicode version |
Description: A positive real is greater than zero. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
rpred.1 |
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Ref | Expression |
---|---|
rpgt0d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpred.1 |
. 2
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2 | rpgt0 9482 |
. 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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rab 2426 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 df-rp 9471 |
This theorem is referenced by: rpregt0d 9520 ltmulgt11d 9549 ltmulgt12d 9550 gt0divd 9551 ge0divd 9552 lediv12ad 9573 expgt0 10357 nnesq 10442 bccl2 10546 resqrexlemp1rp 10810 resqrexlemover 10814 resqrexlemnm 10822 resqrexlemgt0 10824 resqrexlemglsq 10826 sqrtgt0d 10963 reccn2ap 11114 fsumlt 11265 eirraplem 11519 prmind2 11837 sqrt2irrlem 11875 ssblex 12639 mulc1cncf 12784 cncfmptc 12790 mulcncflem 12798 cnplimclemle 12845 pilem3 12912 trilpolemeq1 13408 iooref1o 13426 taupi 13430 |
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