Theorem nulsltsd

Description: The empty set is less-than any set of surreals. Deduction version. (Contributed by Scott Fenton, 27-Feb-2026)

	Ref	Expression
Hypotheses	nulsltsd.1	|- ( ph -> A e. V )
	nulsltsd.2	|- ( ph -> A C_ No )
Assertion	nulsltsd	|- ( ph -> (/) <

Proof

Step	Hyp	Ref	Expression
1		nulsltsd.1	|- ( ph -> A e. V )
2		nulsltsd.2	|- ( ph -> A C_ No )
3	1 2	elpwd	|- ( ph -> A e. ~P No )
4		nulslts	|- ( A e. ~P No -> (/) <
5	3 4	syl	|- ( ph -> (/) <