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Theorem nncni 8742
Description: A positive integer is a complex number. (Contributed by NM, 18-Aug-1999.)
Hypothesis
Ref Expression
nnre.1 𝐴 ∈ ℕ
Assertion
Ref Expression
nncni 𝐴 ∈ ℂ

Proof of Theorem nncni
StepHypRef Expression
1 nnre.1 . . 3 𝐴 ∈ ℕ
21nnrei 8741 . 2 𝐴 ∈ ℝ
32recni 7790 1 𝐴 ∈ ℂ
Colors of variables: wff set class
Syntax hints:  wcel 1480  cc 7630  cn 8732
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-cnex 7723  ax-resscn 7724  ax-1re 7726  ax-addrcl 7729
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-v 2688  df-in 3077  df-ss 3084  df-int 3772  df-inn 8733
This theorem is referenced by:  9p1e10  9196  numnncl2  9216  dec10p  9236  3dec  10473  4bc2eq6  10532  ef01bndlem  11474
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