Theorem nn0xnn0 12505

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 12504	. 2 ⊢ ℕ0 ⊆ ℕ0*
2	1	sseli 3911	1 ⊢ (𝐴 ∈ ℕ0 → 𝐴 ∈ ℕ0*)

Syntax hints:   → wi 4   ∈ wcel 2119  ℕ₀cn0 12428  ℕ₀^*cxnn0 12501

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-v 3433  df-un 3888  df-ss 3900  df-xnn0 12502

This theorem is referenced by:  xnn0xadd0  13190  wlk1ewlk  29726  frgrregorufrg  30414  usgrcyclgt2v  35359