Theorem subsid

Description: Subtraction of a surreal from itself. (Contributed by Scott Fenton, 3-Feb-2025)

	Ref	Expression
Assertion	subsid	|- ( A e. No -> ( A -s A ) = 0s )

Proof

Step	Hyp	Ref	Expression
1		subsval	|- ( ( A e. No /\ A e. No ) -> ( A -s A ) = ( A +s ( -us ` A ) ) )
2	1	anidms	|- ( A e. No -> ( A -s A ) = ( A +s ( -us ` A ) ) )
3		negsid	|- ( A e. No -> ( A +s ( -us ` A ) ) = 0s )
4	2 3	eqtrd	|- ( A e. No -> ( A -s A ) = 0s )