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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 9573 | . 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 clt 7913 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-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-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rab 2444 df-v 2714 df-un 3106 df-sn 3566 df-pr 3567 df-op 3569 df-br 3967 df-rp 9562 |
This theorem is referenced by: rpregt0d 9611 ltmulgt11d 9640 ltmulgt12d 9641 gt0divd 9642 ge0divd 9643 lediv12ad 9664 expgt0 10456 nnesq 10541 bccl2 10646 resqrexlemp1rp 10910 resqrexlemover 10914 resqrexlemnm 10922 resqrexlemgt0 10924 resqrexlemglsq 10926 sqrtgt0d 11063 reccn2ap 11214 fsumlt 11365 eirraplem 11677 dvdsmodexp 11695 prmind2 12001 sqrt2irrlem 12040 modprmn0modprm0 12135 ssblex 12873 mulc1cncf 13018 cncfmptc 13024 mulcncflem 13032 cnplimclemle 13079 pilem3 13146 iooref1o 13647 trilpolemeq1 13653 nconstwlpolemgt0 13676 taupi 13683 |
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