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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 9667 |
. 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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rab 2464 df-v 2741 df-un 3135 df-sn 3600 df-pr 3601 df-op 3603 df-br 4006 df-rp 9656 |
This theorem is referenced by: rpregt0d 9705 ltmulgt11d 9734 ltmulgt12d 9735 gt0divd 9736 ge0divd 9737 lediv12ad 9758 expgt0 10555 nnesq 10642 bccl2 10750 resqrexlemp1rp 11017 resqrexlemover 11021 resqrexlemnm 11029 resqrexlemgt0 11031 resqrexlemglsq 11033 sqrtgt0d 11170 reccn2ap 11323 fsumlt 11474 eirraplem 11786 dvdsmodexp 11804 prmind2 12122 sqrt2irrlem 12163 modprmn0modprm0 12258 ssblex 14016 mulc1cncf 14161 cncfmptc 14167 mulcncflem 14175 cnplimclemle 14222 pilem3 14289 iooref1o 14867 trilpolemeq1 14873 nconstwlpolemgt0 14897 taupi 14906 |
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