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Theorem nn0xnn0d 12606
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 12600 . 2 0 ⊆ ℕ0*
2 nn0xnn0d.1 . 2 (𝜑𝐴 ∈ ℕ0)
31, 2sselid 3993 1 (𝜑𝐴 ∈ ℕ0*)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  0cn0 12524  0*cxnn0 12597
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-un 3968  df-ss 3980  df-xnn0 12598
This theorem is referenced by:  xnn0xaddcl  13274  pcxnn0cl  16894  fusgrn0eqdrusgr  29603  cusgrrusgr  29614
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