Theorem negsidd

Description: Surreal addition of a number and its negative. Theorem 4(iii) of Conway p. 17. (Contributed by Scott Fenton, 5-Feb-2025)

	Ref	Expression
Hypothesis	negsidd.1	$$⊢\phi \to A\in \mathrm{No}$$
Assertion	negsidd	$$⊢\phi \to A{+}_s{+}_s\left(A\right)=0_s$$

Proof

Step	Hyp	Ref	Expression
1		negsidd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		negsid	$$⊢A\in \mathrm{No}\to A{+}_s{+}_s\left(A\right)=0_s$$
3	1 2	syl	$$⊢\phi \to A{+}_s{+}_s\left(A\right)=0_s$$