Theorem sltssn

Description: Surreal set less-than of two singletons. (Contributed by Scott Fenton, 17-Mar-2025)

	Ref	Expression
Hypotheses	sltssn.1	|- ( ph -> A e. No )
	sltssn.2	|- ( ph -> B e. No )
	sltssn.3	|- ( ph -> A
Assertion	sltssn	|- ( ph -> { A } <

Proof

Step	Hyp	Ref	Expression
1		sltssn.1	|- ( ph -> A e. No )
2		sltssn.2	|- ( ph -> B e. No )
3		sltssn.3	|- ( ph -> A
4	1 2	sltssnb	|- ( ph -> ( { A } < A
5	3 4	mpbird	|- ( ph -> { A } <