Theorem rpcn 9854

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 9852	. 2 |- ( A e. RR+ -> A e. RR )
2	1	recnd 8171	1 |- ( A e. RR+ -> A e. CC )

Syntax hints:   -> wi 4   e. wcel 2200   CCcc 7993   RR+crp 9845

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211  ax-resscn 8087

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-rab 2517  df-in 3203  df-ss 3210  df-rp 9846

This theorem is referenced by:  rpcnne0  9865  rpcnap0  9866  divge1  9915  sqrtdiv  11548  efgt1p2  12201  efgt1p  12202  pilem1  15447  rpcxp0  15566  rpcxp1  15567  cxprec  15578  rplogbval  15613  rprelogbdiv  15625