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Theorem nn0xnn0 12603
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 12602 . 2 0 ⊆ ℕ0*
21sseli 3979 1 (𝐴 ∈ ℕ0𝐴 ∈ ℕ0*)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2108  0cn0 12526  0*cxnn0 12599
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-un 3956  df-ss 3968  df-xnn0 12600
This theorem is referenced by:  xnn0xadd0  13289  wlk1ewlk  29658  frgrregorufrg  30345  usgrcyclgt2v  35136
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