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Theorem rpcn 9241
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 9239 . 2 (𝐴 ∈ ℝ+𝐴 ∈ ℝ)
21recnd 7613 1 (𝐴 ∈ ℝ+𝐴 ∈ ℂ)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1445  cc 7445  +crp 9233
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077  ax-resscn 7534
This theorem depends on definitions:  df-bi 116  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-rab 2379  df-in 3019  df-ss 3026  df-rp 9234
This theorem is referenced by:  rpcnne0  9252  rpcnap0  9253  divge1  9299  sqrtdiv  10606  efgt1p2  11150  efgt1p  11151
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