Theorem subsvald

Description: The value of surreal subtraction. (Contributed by Scott Fenton, 5-Feb-2025)

	Ref	Expression
Hypotheses	subsvald.1	|- ( ph -> A e. No )
	subsvald.2	|- ( ph -> B e. No )
Assertion	subsvald	|- ( ph -> ( A -s B ) = ( A +s ( -us ` B ) ) )

Proof

Step	Hyp	Ref	Expression
1		subsvald.1	|- ( ph -> A e. No )
2		subsvald.2	|- ( ph -> B e. No )
3		subsval	|- ( ( A e. No /\ B e. No ) -> ( A -s B ) = ( A +s ( -us ` B ) ) )
4	1 2 3	syl2anc	|- ( ph -> ( A -s B ) = ( A +s ( -us ` B ) ) )