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	$$⊢\phi \to A\in \mathrm{No}$$
Assertion	negscld	$$⊢\phi \to {+}_s\left(A\right)\in \mathrm{No}$$

Proof

Step	Hyp	Ref	Expression
1		negscld.1	$$⊢\phi \to A\in \mathrm{No}$$
2		negscl	$$⊢A\in \mathrm{No}\to {+}_s\left(A\right)\in \mathrm{No}$$
3	1 2	syl	$$⊢\phi \to {+}_s\left(A\right)\in \mathrm{No}$$