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Theorem nn0xnn0d 12608
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 12602 . 2 0 ⊆ ℕ0*
2 nn0xnn0d.1 . 2 (𝜑𝐴 ∈ ℕ0)
31, 2sselid 3981 1 (𝜑𝐴 ∈ 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:  xnn0xaddcl  13277  pcxnn0cl  16898  fusgrn0eqdrusgr  29588  cusgrrusgr  29599
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