Theorem nnn0sd

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

	Ref	Expression
Hypothesis	nnn0sd.1	⊢ ( 𝜑 → 𝐴 ∈ ℕs )
Assertion	nnn0sd	⊢ ( 𝜑 → 𝐴 ∈ ℕ0s )

Proof

Step	Hyp	Ref	Expression
1		nnn0sd.1	⊢ ( 𝜑 → 𝐴 ∈ ℕs )
2		nnssn0s	⊢ ℕs ⊆ ℕ0s
3	2 1	sselid	⊢ ( 𝜑 → 𝐴 ∈ ℕ0s )