Theorem 2onOLD

Description: Obsolete version of 2on as of 30-Nov-2024. (Contributed by NM, 18-Feb-2004) (Proof shortened by Andrew Salmon, 12-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	2onOLD	$$⊢2_{𝑜}\in \mathrm{On}$$

Proof

Step	Hyp	Ref	Expression
1		df-2o	$$⊢2_{𝑜}=\mathrm{suc}{1}_{𝑜}$$
2		1on	$$⊢1_{𝑜}\in \mathrm{On}$$
3	2	onsuci	$$⊢\mathrm{suc}{1}_{𝑜}\in \mathrm{On}$$
4	1 3	eqeltri	$$⊢2_{𝑜}\in \mathrm{On}$$