Theorem nn0xnn0 12603

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 12602	. 2 ⊢ ℕ0 ⊆ ℕ0*
2	1	sseli 3979	1 ⊢ (𝐴 ∈ ℕ0 → 𝐴 ∈ ℕ0*)

Syntax hints:   → wi 4   ∈ wcel 2108  ℕ₀cn0 12526  ℕ₀^*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:  xnn0xadd0  13289  wlk1ewlk  29658  frgrregorufrg  30345  usgrcyclgt2v  35136