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Theorem rpcn 9051
Description: A positive real is a complex number. (Contributed by NM, 11-Nov-2008.)
Assertion
Ref Expression
rpcn (𝐴 ∈ ℝ+𝐴 ∈ ℂ)

Proof of Theorem rpcn
StepHypRef Expression
1 rpre 9049 . 2 (𝐴 ∈ ℝ+𝐴 ∈ ℝ)
21recnd 7437 1 (𝐴 ∈ ℝ+𝐴 ∈ ℂ)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1436  cc 7269  +crp 9043
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067  ax-resscn 7358
This theorem depends on definitions:  df-bi 115  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rab 2364  df-in 2992  df-ss 2999  df-rp 9044
This theorem is referenced by:  rpcnne0  9062  rpcnap0  9063  divge1  9109  sqrtdiv  10316
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