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Theorem nn0ssxnn0 11311
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 3759 . 2 0 ⊆ (ℕ0 ∪ {+∞})
2 df-xnn0 11309 . 2 0* = (ℕ0 ∪ {+∞})
31, 2sseqtr4i 3622 1 0 ⊆ ℕ0*
Colors of variables: wff setvar class
Syntax hints:  cun 3558  wss 3560  {csn 4153  +∞cpnf 10016  0cn0 11237  0*cxnn0 11308
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1841  ax-6 1890  ax-7 1937  ax-9 2001  ax-10 2021  ax-11 2036  ax-12 2049  ax-13 2250  ax-ext 2606
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1883  df-clab 2613  df-cleq 2619  df-clel 2622  df-nfc 2756  df-v 3193  df-un 3565  df-in 3567  df-ss 3574  df-xnn0 11309
This theorem is referenced by:  nn0xnn0  11312  0xnn0  11314  nn0xnn0d  11317
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