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Theorem nn0sscn 9111
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 9110 . 2 0 ⊆ ℝ
2 ax-resscn 7837 . 2 ℝ ⊆ ℂ
31, 2sstri 3147 1 0 ⊆ ℂ
Colors of variables: wff set class
Syntax hints:  wss 3112  cc 7743  cr 7744  0cn0 9106
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 699  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146  ax-sep 4095  ax-cnex 7836  ax-resscn 7837  ax-1re 7839  ax-addrcl 7842  ax-rnegex 7854
This theorem depends on definitions:  df-bi 116  df-tru 1345  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-nfc 2295  df-ral 2447  df-rex 2448  df-v 2724  df-un 3116  df-in 3118  df-ss 3125  df-sn 3577  df-int 3820  df-inn 8850  df-n0 9107
This theorem is referenced by:  nn0cn  9116  nn0expcl  10460  fsumnn0cl  11334  fprodnn0cl  11543  eulerthlemrprm  12150  eulerthlema  12151
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