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Theorem nn0sscn 8430
Description: Nonnegative integers are a subset of the complex numbers.) (Contributed by NM, 9-May-2004.)
Assertion
Ref Expression
nn0sscn  |-  NN0  C_  CC

Proof of Theorem nn0sscn
StepHypRef Expression
1 nn0ssre 8429 . 2  |-  NN0  C_  RR
2 ax-resscn 7200 . 2  |-  RR  C_  CC
31, 2sstri 3017 1  |-  NN0  C_  CC
Colors of variables: wff set class
Syntax hints:    C_ wss 2982   CCcc 7111   RRcr 7112   NN0cn0 8425
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-sep 3916  ax-cnex 7199  ax-resscn 7200  ax-1re 7202  ax-addrcl 7205  ax-rnegex 7217
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-v 2612  df-un 2986  df-in 2988  df-ss 2995  df-sn 3422  df-int 3657  df-inn 8177  df-n0 8426
This theorem is referenced by:  nn0cn  8435  nn0expcl  9657
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