Theorem znegscld

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

	Ref	Expression
Hypothesis	znegscld.1	⊢ ( 𝜑 → 𝐴 ∈ ℤs )
Assertion	znegscld	⊢ ( 𝜑 → ( -us ‘ 𝐴 ) ∈ ℤs )

Proof

Step	Hyp	Ref	Expression
1		znegscld.1	⊢ ( 𝜑 → 𝐴 ∈ ℤs )
2		znegscl	⊢ ( 𝐴 ∈ ℤs → ( -us ‘ 𝐴 ) ∈ ℤs )
3	1 2	syl	⊢ ( 𝜑 → ( -us ‘ 𝐴 ) ∈ ℤs )