Theorem peano2no

Description: A theorem for surreals that is analogous to the second Peano postulate peano2 . (Contributed by Scott Fenton, 17-Mar-2025)

	Ref	Expression
Assertion	peano2no	$$⊢A\in \mathrm{No}\to A{+}_s{1}_s\in \mathrm{No}$$

Proof

Step	Hyp	Ref	Expression
1		1sno	$$⊢1_s\in \mathrm{No}$$
2		addscl	$$⊢\left(A\in \mathrm{No}\wedge 1_s\in \mathrm{No}\right)\to A{+}_s{1}_s\in \mathrm{No}$$
3	1 2	mpan2	$$⊢A\in \mathrm{No}\to A{+}_s{1}_s\in \mathrm{No}$$