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Theorem nnsscn 8919
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 8918 . 2  |-  NN  C_  RR
2 ax-resscn 7899 . 2  |-  RR  C_  CC
31, 2sstri 3164 1  |-  NN  C_  CC
Colors of variables: wff set class
Syntax hints:    C_ wss 3129   CCcc 7805   RRcr 7806   NNcn 8914
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-sep 4120  ax-cnex 7898  ax-resscn 7899  ax-1re 7901  ax-addrcl 7904
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460  df-v 2739  df-in 3135  df-ss 3142  df-int 3845  df-inn 8915
This theorem is referenced by:  nnex  8920  nncn  8922  nncnd  8928  nn0addcl  9206  nn0mulcl  9207  dfz2  9320  nnexpcl  10527  fprodnncl  11610
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