Theorem nn0xnn0 12576

Description: A standard nonnegative integer is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.)

Assertion

Ref	Expression
nn0xnn0	⊢ (𝐴 ∈ ℕ0 → 𝐴 ∈ ℕ0*)

Proof of Theorem nn0xnn0

Step	Hyp	Ref	Expression
1		nn0ssxnn0 12575	. 2 ⊢ ℕ0 ⊆ ℕ0*
2	1	sseli 3933	1 ⊢ (𝐴 ∈ ℕ0 → 𝐴 ∈ ℕ0*)

Syntax hints:   → wi 4   ∈ wcel 2143  ℕ₀cn0 12499  ℕ₀^*cxnn0 12572

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457  df-un 3910  df-ss 3922  df-xnn0 12573

This theorem is referenced by:  xnn0xadd0  13268  wlk1ewlk  29989  frgrregorufrg  30677  usgrcyclgt2v  35623