Theorem nnssnn0 4537

Description: Positive naturals are a subset of nonnegative integers. (Contributed by Raph Levien, 10-Dec-02.)

Assertion

Ref	Expression
nnssnn0	|- NN (_ NN0

Proof of Theorem nnssnn0

Step	Hyp	Ref	Expression
1		ssun1 1621	. 2 |- NN (_ (NN u. {0})
2		df-n0 4535	. 2 |- NN0 = (NN u. {0})
3	1, 2	sseqtr4 1533	1 |- NN (_ NN0

Syntax hints:   u. cun 1485   (_ wss 1487  {csn 1808  0cc0 4028  NNcn 4093  NN0cn0 4094

This theorem is referenced by:  nnnn0t 4541  1nn0 4547  2nn0 4548  nthruz 4785

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-un 1490  df-in 1491  df-ss 1492  df-n0 4535

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