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Theorem nnssnn0 8609
Description: Positive naturals are a subset of nonnegative integers. (Contributed by Raph Levien, 10-Dec-2002.)
Assertion
Ref Expression
nnssnn0 ℕ ⊆ ℕ0

Proof of Theorem nnssnn0
StepHypRef Expression
1 ssun1 3152 . 2 ℕ ⊆ (ℕ ∪ {0})
2 df-n0 8607 . 2 0 = (ℕ ∪ {0})
31, 2sseqtr4i 3048 1 ℕ ⊆ ℕ0
Colors of variables: wff set class
Syntax hints:  cun 2986  wss 2988  {csn 3431  0cc0 7294  cn 8357  0cn0 8606
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617  df-un 2992  df-in 2994  df-ss 3001  df-n0 8607
This theorem is referenced by:  nnnn0  8613  nnnn0d  8659  oddge22np1  10756
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