Theorem nnssnn0 6102

Description: Positive naturals are a subset of nonnegative integers. (Contributed by Raph Levien, 10-Dec-2002.)

Assertion

Ref	Expression
nnssnn0	|- NN (_ NN0

Proof of Theorem nnssnn0

Step	Hyp	Ref	Expression
1		ssun1 2193	. 2 |- NN (_ (NN u. {0})
2		df-n0 6100	. 2 |- NN0 = (NN u. {0})
3	1, 2	sseqtr4 2094	1 |- NN (_ NN0

Syntax hints:   u. cun 2045   (_ wss 2047  {csn 2409  0cc0 5234  NNcn 5296  NN0cn0 5297

This theorem is referenced by:  nnnn0t 6106  nthruz 6746  geolim1i 7238  efseq0ex 7311

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-un 2050  df-in 2051  df-ss 2053  df-n0 6100

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