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Theorem nn0sscn 8243
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 8242 . 2 0 ⊆ ℝ
2 ax-resscn 7033 . 2 ℝ ⊆ ℂ
31, 2sstri 2981 1 0 ⊆ ℂ
Colors of variables: wff set class
Syntax hints:  wss 2944  cc 6944  cr 6945  0cn0 8238
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3902  ax-cnex 7032  ax-resscn 7033  ax-1re 7035  ax-addrcl 7038  ax-rnegex 7050
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rex 2329  df-v 2576  df-un 2949  df-in 2951  df-ss 2958  df-sn 3408  df-int 3643  df-inn 7990  df-n0 8239
This theorem is referenced by:  nn0cn  8248  nn0expcl  9433
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