Theorem onsse

Description: Surreal less-than is set-like over the surreal ordinals. (Contributed by Scott Fenton, 6-Nov-2025)

	Ref	Expression
Assertion	onsse	|-

Proof

Step	Hyp	Ref	Expression
1		epse	|- _E Se On
2		onsiso	|- ( bday |` On_s ) Isom
3		isose	|- ( ( bday |` On_s ) Isom ( _E Se On ) )
4	2 3	ax-mp	|- ( _E Se On )
5	1 4	mpbir	|-