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Theorem nn0xnn0d 11964
Description: A standard nonnegative integer is an extended nonnegative integer, deduction form. (Contributed by AV, 10-Dec-2020.)
Hypothesis
Ref Expression
nn0xnn0d.1 (𝜑𝐴 ∈ ℕ0)
Assertion
Ref Expression
nn0xnn0d (𝜑𝐴 ∈ ℕ0*)

Proof of Theorem nn0xnn0d
StepHypRef Expression
1 nn0ssxnn0 11958 . 2 0 ⊆ ℕ0*
2 nn0xnn0d.1 . 2 (𝜑𝐴 ∈ ℕ0)
31, 2sseldi 3962 1 (𝜑𝐴 ∈ ℕ0*)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2105  0cn0 11885  0*cxnn0 11955
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-v 3494  df-un 3938  df-in 3940  df-ss 3949  df-xnn0 11956
This theorem is referenced by:  xnn0xaddcl  12616  fusgrn0eqdrusgr  27279  cusgrrusgr  27290
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