Metamath Proof Explorer


Theorem nnnod

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

Ref Expression
Hypothesis nnnod.1 ⊢ ( 𝜑 → 𝐴 ∈ ℕs )
Assertion nnnod ( 𝜑 → 𝐴 ∈ No )

Proof

Step Hyp Ref Expression
1 nnnod.1 ⊢ ( 𝜑 → 𝐴 ∈ ℕs )
2 nnno ⊢ ( 𝐴 ∈ ℕs → 𝐴 ∈ No )
3 1 2 syl ⊢ ( 𝜑 → 𝐴 ∈ No )