Theorem nnn0s 28344

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 28338	. 2 ⊢ ℕs ⊆ ℕ0s
2	1	sseli 3918	1 ⊢ (𝐴 ∈ ℕs → 𝐴 ∈ ℕ0s)

Syntax hints:   → wi 4   ∈ wcel 2119  ℕ_0scn0s 28329  ℕ_scnns 28330

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 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-v 3434  df-dif 3893  df-ss 3907  df-nns 28332

This theorem is referenced by:  elzn0s  28415  eln0zs  28417  zseo  28439  addhalfcut  28476  bdaypw2n0bndlem  28480  bdayfinbndlem1  28484  z12bdaylem2  28488  z12sge0  28500