Theorem rpcn 9896

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 9894	. 2 |- ( A e. RR+ -> A e. RR )
2	1	recnd 8207	1 |- ( A e. RR+ -> A e. CC )

Syntax hints:   -> wi 4   e. wcel 2202   CCcc 8029   RR+crp 9887

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213  ax-resscn 8123

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-rab 2519  df-in 3206  df-ss 3213  df-rp 9888

This theorem is referenced by:  rpcnne0  9907  rpcnap0  9908  divge1  9957  sqrtdiv  11602  efgt1p2  12255  efgt1p  12256  pilem1  15502  rpcxp0  15621  rpcxp1  15622  cxprec  15633  rplogbval  15668  rprelogbdiv  15680