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Theorem nn0xnn0 11963
 Description: A standard nonnegative integer is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.)
Assertion
Ref Expression
nn0xnn0 (𝐴 ∈ ℕ0𝐴 ∈ ℕ0*)

Proof of Theorem nn0xnn0
StepHypRef Expression
1 nn0ssxnn0 11962 . 2 0 ⊆ ℕ0*
21sseli 3914 1 (𝐴 ∈ ℕ0𝐴 ∈ ℕ0*)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2112  ℕ0cn0 11889  ℕ0*cxnn0 11959 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-ext 2773 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-v 3446  df-un 3889  df-in 3891  df-ss 3901  df-xnn0 11960 This theorem is referenced by:  xnn0xadd0  12632  wlk1ewlk  27432  frgrregorufrg  28114  usgrcyclgt2v  32486
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