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Theorem nnssnn0 8184
 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 3106 . 2 ℕ ⊆ (ℕ ∪ {0})
2 df-n0 8182 . 2 0 = (ℕ ∪ {0})
31, 2sseqtr4i 2978 1 ℕ ⊆ ℕ0
 Colors of variables: wff set class Syntax hints:   ∪ cun 2915   ⊆ wss 2917  {csn 3375  0cc0 6889  ℕcn 7914  ℕ0cn0 8181 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-n0 8182 This theorem is referenced by:  nnnn0  8188  nnnn0d  8235
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