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Theorem rpcn 8591
 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 8589 . 2 (𝐴 ∈ ℝ+𝐴 ∈ ℝ)
21recnd 7054 1 (𝐴 ∈ ℝ+𝐴 ∈ ℂ)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1393  ℂcc 6887  ℝ+crp 8583 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-resscn 6976 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rab 2315  df-in 2924  df-ss 2931  df-rp 8584 This theorem is referenced by:  rpcnne0  8602  rpcnap0  8603  divge1  8649  sqrtdiv  9640
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