Theorem rpcn 9941

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 9939	. 2 |- ( A e. RR+ -> A e. RR )
2	1	recnd 8250	1 |- ( A e. RR+ -> A e. CC )

Syntax hints:   -> wi 4   e. wcel 2202   CCcc 8073   RR+crp 9932

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213  ax-resscn 8167

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-rab 2520  df-in 3207  df-ss 3214  df-rp 9933

This theorem is referenced by:  rpcnne0  9952  rpcnap0  9953  divge1  10002  sqrtdiv  11665  efgt1p2  12319  efgt1p  12320  pilem1  15573  rpcxp0  15692  rpcxp1  15693  cxprec  15704  rplogbval  15739  rprelogbdiv  15751