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Theorem nn0ssxnn0 8739
Description: The standard nonnegative integers are a subset of the extended nonnegative integers. (Contributed by AV, 10-Dec-2020.)
Assertion
Ref Expression
nn0ssxnn0 0 ⊆ ℕ0*

Proof of Theorem nn0ssxnn0
StepHypRef Expression
1 ssun1 3163 . 2 0 ⊆ (ℕ0 ∪ {+∞})
2 df-xnn0 8737 . 2 0* = (ℕ0 ∪ {+∞})
31, 2sseqtr4i 3059 1 0 ⊆ ℕ0*
Colors of variables: wff set class
Syntax hints:  cun 2997  wss 2999  {csn 3446  +∞cpnf 7519  0cn0 8673  0*cxnn0 8736
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3003  df-in 3005  df-ss 3012  df-xnn0 8737
This theorem is referenced by:  nn0xnn0  8740  0xnn0  8742  nn0xnn0d  8745
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