Theorem negscld

Description: The surreals are closed under negation. Theorem 6(ii) of Conway p. 18. (Contributed by Scott Fenton, 3-Feb-2025)

	Ref	Expression
Hypothesis	negscld.1	|- ( ph -> A e. No )
Assertion	negscld	|- ( ph -> ( -us ` A ) e. No )

Proof

Step	Hyp	Ref	Expression
1		negscld.1	|- ( ph -> A e. No )
2		negscl	|- ( A e. No -> ( -us ` A ) e. No )
3	1 2	syl	|- ( ph -> ( -us ` A ) e. No )