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Theorem nn0xnn0 11559
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 11558 . 2 0 ⊆ ℕ0*
21sseli 3740 1 (𝐴 ∈ ℕ0𝐴 ∈ ℕ0*)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2139  0cn0 11484  0*cxnn0 11555
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-v 3342  df-un 3720  df-in 3722  df-ss 3729  df-xnn0 11556
This theorem is referenced by:  xnn0xadd0  12270  wlk1ewlk  26746  frgrregorufrg  27480
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