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Theorem nnsscn 8399
Description: The positive integers are a subset of the complex numbers. (Contributed by NM, 2-Aug-2004.)
Assertion
Ref Expression
nnsscn  |-  NN  C_  CC

Proof of Theorem nnsscn
StepHypRef Expression
1 nnssre 8398 . 2  |-  NN  C_  RR
2 ax-resscn 7416 . 2  |-  RR  C_  CC
31, 2sstri 3032 1  |-  NN  C_  CC
Colors of variables: wff set class
Syntax hints:    C_ wss 2997   CCcc 7327   RRcr 7328   NNcn 8394
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3949  ax-cnex 7415  ax-resscn 7416  ax-1re 7418  ax-addrcl 7421
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-v 2621  df-in 3003  df-ss 3010  df-int 3684  df-inn 8395
This theorem is referenced by:  nnex  8400  nncn  8402  nncnd  8408  nn0addcl  8678  nn0mulcl  8679  dfz2  8789  nnexpcl  9933
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