Theorem ltsnled

Description: Surreal less-than in terms of less-than or equal. Deduction version. (Contributed by Scott Fenton, 25-Feb-2026)

	Ref	Expression
Hypotheses	lesd.1	|- ( ph -> A e. No )
	lesd.2	|- ( ph -> B e. No )
Assertion	ltsnled	|- ( ph -> ( A -. B <_s A ) )

Proof

Step	Hyp	Ref	Expression
1		lesd.1	|- ( ph -> A e. No )
2		lesd.2	|- ( ph -> B e. No )
3		ltnles	|- ( ( A e. No /\ B e. No ) -> ( A -. B <_s A ) )
4	1 2 3	syl2anc	|- ( ph -> ( A -. B <_s A ) )