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Theorem rpregt0 10367
Description: A positive real is a positive real number. (Contributed by NM, 11-Nov-2008.) (Revised by Mario Carneiro, 31-Jan-2014.)
Assertion
Ref Expression
rpregt0  |-  ( A  e.  RR+  ->  ( A  e.  RR  /\  0  <  A ) )

Proof of Theorem rpregt0
StepHypRef Expression
1 elrp 10356 . 2  |-  ( A  e.  RR+  <->  ( A  e.  RR  /\  0  < 
A ) )
21biimpi 186 1  |-  ( A  e.  RR+  ->  ( A  e.  RR  /\  0  <  A ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    e. wcel 1684   class class class wbr 4023   RRcr 8736   0cc0 8737    < clt 8867   RR+crp 10354
This theorem is referenced by:  rpne0  10369  modge0  10980  modlt  10981  modid  10993  expnlbnd  11231  o1fsum  12271  isprm6  12788  gexexlem  15144  lmnn  18689  aaliou2b  19721  harmonicbnd4  20304  logfaclbnd  20461  logfacrlim  20463  chto1ub  20625  vmadivsum  20631  dchrmusumlema  20642  dchrvmasumlem2  20647  dchrisum0lem2a  20666  dchrisum0lem2  20667  dchrisum0lem3  20668  mulogsumlem  20680  mulog2sumlem2  20684  selberg2lem  20699  selberg3lem1  20706  pntrmax  20713  pntrsumo1  20714  pntibndlem3  20741  equivbnd  26514
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-rp 10355
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