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Theorem nnsscn 8362
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 8361 . 2 ℕ ⊆ ℝ
2 ax-resscn 7381 . 2 ℝ ⊆ ℂ
31, 2sstri 3023 1 ℕ ⊆ ℂ
Colors of variables: wff set class
Syntax hints:  wss 2988  cc 7292  cr 7293  cn 8357
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067  ax-sep 3932  ax-cnex 7380  ax-resscn 7381  ax-1re 7383  ax-addrcl 7386
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-ral 2360  df-v 2617  df-in 2994  df-ss 3001  df-int 3672  df-inn 8358
This theorem is referenced by:  nnex  8363  nncn  8365  nncnd  8371  nn0addcl  8641  nn0mulcl  8642  dfz2  8752  nnexpcl  9866
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