Theorem rpcn 9995

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 9993	. 2 |- ( A e. RR+ -> A e. RR )
2	1	recnd 8302	1 |- ( A e. RR+ -> A e. CC )

Syntax hints:   -> wi 4   e. wcel 2203   CCcc 8125   RR+crp 9986

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 2214  ax-resscn 8219

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-rab 2529  df-in 3217  df-ss 3224  df-rp 9987

This theorem is referenced by:  rpcnne0  10006  rpcnap0  10007  divge1  10056  sqrtdiv  11727  efgt1p2  12381  efgt1p  12382  pilem1  15644  rpcxp0  15763  rpcxp1  15764  cxprec  15775  rplogbval  15810  rprelogbdiv  15822