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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 9206 |
. 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-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-rab 2369 df-v 2622 df-un 3004 df-sn 3456 df-pr 3457 df-op 3459 df-br 3852 df-rp 9196 |
This theorem is referenced by: rpregt0d 9241 ltmulgt11d 9270 ltmulgt12d 9271 gt0divd 9272 ge0divd 9273 lediv12ad 9294 expgt0 10049 nnesq 10134 bccl2 10237 resqrexlemp1rp 10500 resqrexlemover 10504 resqrexlemnm 10512 resqrexlemgt0 10514 resqrexlemglsq 10516 sqrtgt0d 10653 fsumlt 10919 eirraplem 11125 prmind2 11441 sqrt2irrlem 11479 mulc1cncf 11918 |
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