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	|- ( ph -> A e. NN0_s )
Assertion	peano2n0sd	|- ( ph -> ( A +s 1s ) e. NN0_s )

Proof

Step	Hyp	Ref	Expression
1		peano2n0sd.1	|- ( ph -> A e. NN0_s )
2		peano2n0s	|- ( A e. NN0_s -> ( A +s 1s ) e. NN0_s )
3	1 2	syl	|- ( ph -> ( A +s 1s ) e. NN0_s )