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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
StepHypRef Expression
1 ssun1 3666 . 2
2 df-n0 10821 . 2
31, 2sseqtr4i 3536 1
Colors of variables: wff setvar class
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
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