Theorem addsridd

Description: Surreal addition to zero is identity. Part of Theorem 3 of Conway p. 17. (Contributed by Scott Fenton, 20-Aug-2024)

	Ref	Expression
Hypothesis	addsridd.1	$$⊢\phi \to A\in \mathrm{No}$$
Assertion	addsridd	$$⊢\phi \to A{+}_s{0}_s=A$$

Proof

Step	Hyp	Ref	Expression
1		addsridd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		addsrid	$$⊢A\in \mathrm{No}\to A{+}_s{0}_s=A$$
3	1 2	syl	$$⊢\phi \to A{+}_s{0}_s=A$$