Theorem nnssnn0 10823

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

Assertion

Ref	Expression
nnssnn0

Proof of Theorem nnssnn0

Step	Hyp	Ref	Expression
1		ssun1 3666	. 2
2		df-n0 10821	. 2
3	1, 2	sseqtr4i 3536	1

Syntax hints:  u.cun 3473  C_wss 3475  {csn 4029  0cc0 9513  cn 10561  cn0 10820

This theorem is referenced by:  nnnn0  10827  nnnn0d  10877  nthruz  13985  bitsfzolem  14084  ramub1  14546  ramcl  14547  ply1divex  22537  pserdvlem2  22823  hbtlem5  31077  fourierdlem50  31939  fourierdlem102  31991  fourierdlem114  32003

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-in 3482  df-ss 3489  df-n0 10821