Metamath Proof Explorer


Theorem n0nod

Description: A non-negative surreal integer is a surreal. (Contributed by Scott Fenton, 15-Apr-2025)

Ref Expression
Hypothesis n0nod.1 ⊢ ( 𝜑 → 𝐴 ∈ ℕ0s )
Assertion n0nod ( 𝜑 → 𝐴 ∈ No )

Proof

Step Hyp Ref Expression
1 n0nod.1 ⊢ ( 𝜑 → 𝐴 ∈ ℕ0s )
2 n0no ⊢ ( 𝐴 ∈ ℕ0s → 𝐴 ∈ No )
3 1 2 syl ⊢ ( 𝜑 → 𝐴 ∈ No )