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Theorem nnsscn 7917
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 7916 . 2  |-  NN  C_  RR
2 ax-resscn 6974 . 2  |-  RR  C_  CC
31, 2sstri 2954 1  |-  NN  C_  CC
Colors of variables: wff set class
Syntax hints:    C_ wss 2917   CCcc 6885   RRcr 6886   NNcn 7912
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-cnex 6973  ax-resscn 6974  ax-1re 6976  ax-addrcl 6979
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559  df-in 2924  df-ss 2931  df-int 3616  df-inn 7913
This theorem is referenced by:  nnex  7918  nncn  7920  nncnd  7926  nn0addcl  8215  nn0mulcl  8216  dfz2  8311  nnexpcl  9242
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