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Theorem rpregt0 10625
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 10614 . 2  |-  ( A  e.  RR+  <->  ( A  e.  RR  /\  0  < 
A ) )
21biimpi 187 1  |-  ( A  e.  RR+  ->  ( A  e.  RR  /\  0  <  A ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    e. wcel 1725   class class class wbr 4212   RRcr 8989   0cc0 8990    < clt 9120   RR+crp 10612
This theorem is referenced by:  rpne0  10627  modge0  11257  modlt  11258  modid  11270  expnlbnd  11509  o1fsum  12592  isprm6  13109  gexexlem  15467  lmnn  19216  aaliou2b  20258  harmonicbnd4  20849  logfaclbnd  21006  logfacrlim  21008  chto1ub  21170  vmadivsum  21176  dchrmusumlema  21187  dchrvmasumlem2  21192  dchrisum0lem2a  21211  dchrisum0lem2  21212  dchrisum0lem3  21213  mulogsumlem  21225  mulog2sumlem2  21229  selberg2lem  21244  selberg3lem1  21251  pntrmax  21258  pntrsumo1  21259  pntibndlem3  21286
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-rp 10613
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