Theorem negsidd

Description: Surreal addition of a number and its negative. Theorem 4(iii) of Conway p. 17. (Contributed by Scott Fenton, 5-Feb-2025)

	Ref	Expression
Hypothesis	negsidd.1	|- ( ph -> A e. No )
Assertion	negsidd	|- ( ph -> ( A +s ( -us ` A ) ) = 0s )

Proof

Step	Hyp	Ref	Expression
1		negsidd.1	|- ( ph -> A e. No )
2		negsid	|- ( A e. No -> ( A +s ( -us ` A ) ) = 0s )
3	1 2	syl	|- ( ph -> ( A +s ( -us ` A ) ) = 0s )