Theorem rpcn 9819

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

Step	Hyp	Ref	Expression
1		rpre 9817	. 2 |- ( A e. RR+ -> A e. RR )
2	1	recnd 8136	1 |- ( A e. RR+ -> A e. CC )

Syntax hints:   -> wi 4   e. wcel 2178   CCcc 7958   RR+crp 9810

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189  ax-resscn 8052

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-rab 2495  df-in 3180  df-ss 3187  df-rp 9811

This theorem is referenced by:  rpcnne0  9830  rpcnap0  9831  divge1  9880  sqrtdiv  11468  efgt1p2  12121  efgt1p  12122  pilem1  15366  rpcxp0  15485  rpcxp1  15486  cxprec  15497  rplogbval  15532  rprelogbdiv  15544