Theorem subscld

Description: Closure law for surreal subtraction. (Contributed by Scott Fenton, 5-Feb-2025)

	Ref	Expression
Hypotheses	subscld.1	|- ( ph -> A e. No )
	subscld.2	|- ( ph -> B e. No )
Assertion	subscld	|- ( ph -> ( A -s B ) e. No )

Proof

Step	Hyp	Ref	Expression
1		subscld.1	|- ( ph -> A e. No )
2		subscld.2	|- ( ph -> B e. No )
3		subscl	|- ( ( A e. No /\ B e. No ) -> ( A -s B ) e. No )
4	1 2 3	syl2anc	|- ( ph -> ( A -s B ) e. No )