Theorem peano2n0sd

Description: Peano postulate: the successor of a non-negative surreal integer is a non-negative surreal integer. Deduction form. (Contributed by Scott Fenton, 27-Feb-2026)

	Ref	Expression
Hypothesis	peano2n0sd.1	⊢ ( 𝜑 → 𝐴 ∈ ℕ0s )
Assertion	peano2n0sd	⊢ ( 𝜑 → ( 𝐴 +s 1s ) ∈ ℕ0s )

Proof

Step	Hyp	Ref	Expression
1		peano2n0sd.1	⊢ ( 𝜑 → 𝐴 ∈ ℕ0s )
2		peano2n0s	⊢ ( 𝐴 ∈ ℕ0s → ( 𝐴 +s 1s ) ∈ ℕ0s )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 +s 1s ) ∈ ℕ0s )