Theorem nnn0s 28743

Description: A positive surreal integer is a non-negative surreal integer. (Contributed by Scott Fenton, 26-May-2025.)

Assertion

Ref	Expression
nnn0s	⊢ (𝐴 ∈ ℕs → 𝐴 ∈ ℕ0s)

Proof of Theorem nnn0s

Step	Hyp	Ref	Expression
1		nnssn0s 28737	. 2 ⊢ ℕs ⊆ ℕ0s
2	1	sseli 3909	1 ⊢ (𝐴 ∈ ℕs → 𝐴 ∈ ℕ0s)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2147  ℕ_0scn0s 28728  ℕ_scnns 28729

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-dif 4050  df-nns 28731

This theorem is used by:  elzn0s  28814  eln0zs  28816  zseo  28838  addhalfcut  28875  bdaypw2n0bndlem  28879  bdayfinbndlem1  28883  z12bdaylem2  28887  z12sge0  28899