Theorem ltsubs1d

Description: Subtraction from both sides of surreal less-than. (Contributed by Scott Fenton, 5-Feb-2025)

	Ref	Expression
Hypotheses	ltsubsd.1	|- ( ph -> A e. No )
	ltsubsd.2	|- ( ph -> B e. No )
	ltsubsd.3	|- ( ph -> C e. No )
Assertion	ltsubs1d	|- ( ph -> ( A ( A -s C )

Proof

Step	Hyp	Ref	Expression
1		ltsubsd.1	|- ( ph -> A e. No )
2		ltsubsd.2	|- ( ph -> B e. No )
3		ltsubsd.3	|- ( ph -> C e. No )
4		ltsubs1	|- ( ( A e. No /\ B e. No /\ C e. No ) -> ( A ( A -s C )
5	1 2 3 4	syl3anc	|- ( ph -> ( A ( A -s C )