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Theorem nnsscn 7919
Description: The positive integers are a subset of the complex numbers. (Contributed by NM, 2-Aug-2004.)
Assertion
Ref Expression
nnsscn ℕ ⊆ ℂ

Proof of Theorem nnsscn
StepHypRef Expression
1 nnssre 7918 . 2 ℕ ⊆ ℝ
2 ax-resscn 6976 . 2 ℝ ⊆ ℂ
31, 2sstri 2954 1 ℕ ⊆ ℂ
Colors of variables: wff set class
Syntax hints:  wss 2917  cc 6887  cr 6888  cn 7914
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-sep 3875  ax-cnex 6975  ax-resscn 6976  ax-1re 6978  ax-addrcl 6981
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559  df-in 2924  df-ss 2931  df-int 3616  df-inn 7915
This theorem is referenced by:  nnex  7920  nncn  7922  nncnd  7928  nn0addcl  8217  nn0mulcl  8218  dfz2  8313  nnexpcl  9268
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