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Theorem rpgt0 8878
Description: A positive real is greater than zero. (Contributed by FL, 27-Dec-2007.)
Assertion
Ref Expression
rpgt0  |-  ( A  e.  RR+  ->  0  < 
A )

Proof of Theorem rpgt0
StepHypRef Expression
1 elrp 8869 . 2  |-  ( A  e.  RR+  <->  ( A  e.  RR  /\  0  < 
A ) )
21simprbi 269 1  |-  ( A  e.  RR+  ->  0  < 
A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1434   class class class wbr 3805   RRcr 7094   0cc0 7095    < clt 7267   RR+crp 8867
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 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-rab 2362  df-v 2612  df-un 2986  df-sn 3422  df-pr 3423  df-op 3425  df-br 3806  df-rp 8868
This theorem is referenced by:  rpge0  8879  rpap0  8883  rpgecl  8895  0nrp  8900  rpgt0d  8909  addlelt  8972  rpsqrtcl  10128  climconst  10330
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