Theorem 0no

Description: Ordinal zero maps to a surreal number. (Contributed by RP, 21-Sep-2023)

	Ref	Expression
Assertion	0no	$$⊢\varnothing \in \mathrm{No}$$

Proof

Step	Hyp	Ref	Expression
1		0xp	$$⊢\varnothing \times \left\{2_{𝑜}\right\}=\varnothing$$
2		0elon	$$⊢\varnothing \in \mathrm{On}$$
3	2	onnoi	$$⊢\varnothing \times \left\{2_{𝑜}\right\}\in \mathrm{No}$$
4	1 3	eqeltrri	$$⊢\varnothing \in \mathrm{No}$$