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Theorem rpcn 9664
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 9662 . 2  |-  ( A  e.  RR+  ->  A  e.  RR )
21recnd 7988 1  |-  ( A  e.  RR+  ->  A  e.  CC )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2148   CCcc 7811   RR+crp 9655
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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-resscn 7905
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rab 2464  df-in 3137  df-ss 3144  df-rp 9656
This theorem is referenced by:  rpcnne0  9675  rpcnap0  9676  divge1  9725  sqrtdiv  11053  efgt1p2  11705  efgt1p  11706  pilem1  14285  rpcxp0  14404  rpcxp1  14405  cxprec  14416  rplogbval  14448  rprelogbdiv  14460
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