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Theorem rpgt0 9465
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 9455 . 2  |-  ( A  e.  RR+  <->  ( A  e.  RR  /\  0  < 
A ) )
21simprbi 273 1  |-  ( A  e.  RR+  ->  0  < 
A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1480   class class class wbr 3929   RRcr 7631   0cc0 7632    < clt 7812   RR+crp 9453
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rab 2425  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930  df-rp 9454
This theorem is referenced by:  rpge0  9466  rpap0  9470  rpgecl  9482  0nrp  9489  rpgt0d  9498  addlelt  9567  rpsqrtcl  10825  rpmaxcl  11007  rpmincl  11021  xrminrpcl  11055  climconst  11071  blcntrps  12598  blcntr  12599  bdmet  12685  bdmopn  12687  reeff1o  12877  coseq00topi  12938  coseq0negpitopi  12939
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