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Theorem nn0sscn 8186
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 8185 . 2 0 ⊆ ℝ
2 ax-resscn 6976 . 2 ℝ ⊆ ℂ
31, 2sstri 2954 1 0 ⊆ ℂ
Colors of variables: wff set class
Syntax hints:  wss 2917  cc 6887  cr 6888  0cn0 8181
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 6975  ax-resscn 6976  ax-1re 6978  ax-addrcl 6981  ax-rnegex 6993
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-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-sn 3381  df-int 3616  df-inn 7915  df-n0 8182
This theorem is referenced by:  nn0cn  8191  nn0expcl  9269
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