Theorem znegscld

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

	Ref	Expression
Hypothesis	znegscld.1	$$⊢\phi \to A\in {\mathbb{Z}}_s$$
Assertion	znegscld	$$⊢\phi \to {+}_s\left(A\right)\in {\mathbb{Z}}_s$$

Proof

Step	Hyp	Ref	Expression
1		znegscld.1	$$⊢\phi \to A\in {\mathbb{Z}}_s$$
2		znegscl	$$⊢A\in {\mathbb{Z}}_s\to {+}_s\left(A\right)\in {\mathbb{Z}}_s$$
3	1 2	syl	$$⊢\phi \to {+}_s\left(A\right)\in {\mathbb{Z}}_s$$