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Theorem nnsscn 8737
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 8736 . 2  |-  NN  C_  RR
2 ax-resscn 7724 . 2  |-  RR  C_  CC
31, 2sstri 3106 1  |-  NN  C_  CC
Colors of variables: wff set class
Syntax hints:    C_ wss 3071   CCcc 7630   RRcr 7631   NNcn 8732
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-cnex 7723  ax-resscn 7724  ax-1re 7726  ax-addrcl 7729
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-v 2688  df-in 3077  df-ss 3084  df-int 3772  df-inn 8733
This theorem is referenced by:  nnex  8738  nncn  8740  nncnd  8746  nn0addcl  9024  nn0mulcl  9025  dfz2  9135  nnexpcl  10318
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