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Theorem rpcn 9694
Description: A positive real is a complex number. (Contributed by NM, 11-Nov-2008.)
Assertion
Ref Expression
rpcn  |-  ( A  e.  RR+  ->  A  e.  CC )

Proof of Theorem rpcn
StepHypRef Expression
1 rpre 9692 . 2  |-  ( A  e.  RR+  ->  A  e.  RR )
21recnd 8017 1  |-  ( A  e.  RR+  ->  A  e.  CC )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2160   CCcc 7840   RR+crp 9685
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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-resscn 7934
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-rab 2477  df-in 3150  df-ss 3157  df-rp 9686
This theorem is referenced by:  rpcnne0  9705  rpcnap0  9706  divge1  9755  sqrtdiv  11086  efgt1p2  11738  efgt1p  11739  pilem1  14677  rpcxp0  14796  rpcxp1  14797  cxprec  14808  rplogbval  14840  rprelogbdiv  14852
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