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Theorem nnsscn 7995
 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 7994 . 2 ℕ ⊆ ℝ
2 ax-resscn 7034 . 2 ℝ ⊆ ℂ
31, 2sstri 2982 1 ℕ ⊆ ℂ
 Colors of variables: wff set class Syntax hints:   ⊆ wss 2945  ℂcc 6945  ℝcr 6946  ℕcn 7990 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903  ax-cnex 7033  ax-resscn 7034  ax-1re 7036  ax-addrcl 7039 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-v 2576  df-in 2952  df-ss 2959  df-int 3644  df-inn 7991 This theorem is referenced by:  nnex  7996  nncn  7998  nncnd  8004  nn0addcl  8274  nn0mulcl  8275  dfz2  8371  nnexpcl  9433
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