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	$$⊢\phi \to A\in {\mathbb{N}}_{\mathrm{0s}}$$
Assertion	peano2n0sd	$$⊢\phi \to A{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$

Proof

Step	Hyp	Ref	Expression
1		peano2n0sd.1	$$⊢\phi \to A\in {\mathbb{N}}_{\mathrm{0s}}$$
2		peano2n0s	$$⊢A\in {\mathbb{N}}_{\mathrm{0s}}\to A{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$
3	1 2	syl	$$⊢\phi \to A{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$