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Theorem nn0sscn 8940
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 8939 . 2  |-  NN0  C_  RR
2 ax-resscn 7680 . 2  |-  RR  C_  CC
31, 2sstri 3076 1  |-  NN0  C_  CC
Colors of variables: wff set class
Syntax hints:    C_ wss 3041   CCcc 7586   RRcr 7587   NN0cn0 8935
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-sep 4016  ax-cnex 7679  ax-resscn 7680  ax-1re 7682  ax-addrcl 7685  ax-rnegex 7697
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-ral 2398  df-rex 2399  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-sn 3503  df-int 3742  df-inn 8685  df-n0 8936
This theorem is referenced by:  nn0cn  8945  nn0expcl  10262  fsumnn0cl  11127
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