Theorem znegscld

Description: The surreal integers are closed under negation. (Contributed by Scott Fenton, 26-May-2025)

	Ref	Expression
Hypothesis	znegscld.1	|- ( ph -> A e. ZZ_s )
Assertion	znegscld	|- ( ph -> ( -us ` A ) e. ZZ_s )

Proof

Step	Hyp	Ref	Expression
1		znegscld.1	|- ( ph -> A e. ZZ_s )
2		znegscl	|- ( A e. ZZ_s -> ( -us ` A ) e. ZZ_s )
3	1 2	syl	|- ( ph -> ( -us ` A ) e. ZZ_s )