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Theorem nnn0s 28333
Description: A positive surreal integer is a non-negative surreal integer. (Contributed by Scott Fenton, 26-May-2025.)
Assertion
Ref Expression
nnn0s (𝐴 ∈ ℕs𝐴 ∈ ℕ0s)

Proof of Theorem nnn0s
StepHypRef Expression
1 nnssn0s 28327 . 2 s ⊆ ℕ0s
21sseli 3978 1 (𝐴 ∈ ℕs𝐴 ∈ ℕ0s)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  0scnn0s 28319  scnns 28320
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-dif 3953  df-ss 3967  df-nns 28322
This theorem is referenced by:  elzn0s  28385  eln0zs  28387  zseo  28407  addhalfcut  28420
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