Theorem 2onn

Description: The ordinal 2 is a natural number. (Contributed by NM, 28-Sep-2004)

	Ref	Expression
Assertion	2onn	$$⊢2_{𝑜}\in \mathrm{\omega }$$

Proof

Step	Hyp	Ref	Expression
1		df-2o	$$⊢2_{𝑜}=\mathrm{suc}{1}_{𝑜}$$
2		1onn	$$⊢1_{𝑜}\in \mathrm{\omega }$$
3		peano2	$$⊢1_{𝑜}\in \mathrm{\omega }\to \mathrm{suc}{1}_{𝑜}\in \mathrm{\omega }$$
4	2 3	ax-mp	$$⊢\mathrm{suc}{1}_{𝑜}\in \mathrm{\omega }$$
5	1 4	eqeltri	$$⊢2_{𝑜}\in \mathrm{\omega }$$