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Theorem nnssnn0 8241
 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 3133 . 2 ℕ ⊆ (ℕ ∪ {0})
2 df-n0 8239 . 2 0 = (ℕ ∪ {0})
31, 2sseqtr4i 3005 1 ℕ ⊆ ℕ0
 Colors of variables: wff set class Syntax hints:   ∪ cun 2942   ⊆ wss 2944  {csn 3402  0cc0 6946  ℕcn 7989  ℕ0cn0 8238 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2949  df-in 2951  df-ss 2958  df-n0 8239 This theorem is referenced by:  nnnn0  8245  nnnn0d  8291  oddge22np1  10192
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