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Theorem rpcnd 8399
Description: A positive real is a complex number. (Contributed by Mario Carneiro, 28-May-2016.)
Hypothesis
Ref Expression
rpred.1 (φA +)
Assertion
Ref Expression
rpcnd (φA ℂ)

Proof of Theorem rpcnd
StepHypRef Expression
1 rpred.1 . . 3 (φA +)
21rpred 8397 . 2 (φA ℝ)
32recnd 6851 1 (φA ℂ)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1390  cc 6709  +crp 8358
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-resscn 6775
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rab 2309  df-in 2918  df-ss 2925  df-rp 8359
This theorem is referenced by:  rpcnne0d  8406  ltaddrp2d  8427  iccf1o  8642
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