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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 |
Ref | Expression |
---|---|
rpgt0d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpred.1 | . 2 | |
2 | rpgt0 8745 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1433 class class class wbr 3785 cc0 6981 clt 7153 crp 8734 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rab 2357 df-v 2603 df-un 2977 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 df-rp 8735 |
This theorem is referenced by: rpregt0d 8780 ltmulgt11d 8809 ltmulgt12d 8810 gt0divd 8811 ge0divd 8812 lediv12ad 8833 expgt0 9509 nnesq 9592 bccl2 9695 resqrexlemp1rp 9892 resqrexlemover 9896 resqrexlemnm 9904 resqrexlemgt0 9906 resqrexlemglsq 9908 sqrtgt0d 10045 prmind2 10502 sqrt2irrlem 10540 |
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