Theorem rpcn 9783

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 9781	. 2 |- ( A e. RR+ -> A e. RR )
2	1	recnd 8100	1 |- ( A e. RR+ -> A e. CC )

Syntax hints:   -> wi 4   e. wcel 2175   CCcc 7922   RR+crp 9774

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 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186  ax-resscn 8016

This theorem depends on definitions:  df-bi 117  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-nfc 2336  df-rab 2492  df-in 3171  df-ss 3178  df-rp 9775

This theorem is referenced by:  rpcnne0  9794  rpcnap0  9795  divge1  9844  sqrtdiv  11324  efgt1p2  11977  efgt1p  11978  pilem1  15222  rpcxp0  15341  rpcxp1  15342  cxprec  15353  rplogbval  15388  rprelogbdiv  15400