Theorem onnoi

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

	Ref	Expression
Hypothesis	onnoi.on	$$⊢A\in \mathrm{On}$$
Assertion	onnoi	$$⊢A\times \left\{2_{𝑜}\right\}\in \mathrm{No}$$

Proof

Step	Hyp	Ref	Expression
1		onnoi.on	$$⊢A\in \mathrm{On}$$
2		onno	$$⊢A\in \mathrm{On}\to A\times \left\{2_{𝑜}\right\}\in \mathrm{No}$$
3	1 2	ax-mp	$$⊢A\times \left\{2_{𝑜}\right\}\in \mathrm{No}$$