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Theorem nn0ssxnn0 11404
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 3809 . 2 0 ⊆ (ℕ0 ∪ {+∞})
2 df-xnn0 11402 . 2 0* = (ℕ0 ∪ {+∞})
31, 2sseqtr4i 3671 1 0 ⊆ ℕ0*
Colors of variables: wff setvar class
Syntax hints:  cun 3605  wss 3607  {csn 4210  +∞cpnf 10109  0cn0 11330  0*cxnn0 11401
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-un 3612  df-in 3614  df-ss 3621  df-xnn0 11402
This theorem is referenced by:  nn0xnn0  11405  0xnn0  11407  nn0xnn0d  11410
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