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Theorem nn0sscn 8996
Description: Nonnegative integers are a subset of the complex numbers.) (Contributed by NM, 9-May-2004.)
Assertion
Ref Expression
nn0sscn 0 ⊆ ℂ

Proof of Theorem nn0sscn
StepHypRef Expression
1 nn0ssre 8995 . 2 0 ⊆ ℝ
2 ax-resscn 7726 . 2 ℝ ⊆ ℂ
31, 2sstri 3106 1 0 ⊆ ℂ
Colors of variables: wff set class
Syntax hints:  wss 3071  cc 7632  cr 7633  0cn0 8991
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 7725  ax-resscn 7726  ax-1re 7728  ax-addrcl 7731  ax-rnegex 7743
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-rex 2422  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-sn 3533  df-int 3772  df-inn 8735  df-n0 8992
This theorem is referenced by:  nn0cn  9001  nn0expcl  10321  fsumnn0cl  11186
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