Theorem 2oex

Description: 2o is a set. (Contributed by BJ, 6-Apr-2019) Remove dependency on ax-10 , ax-11 , ax-12 , ax-un . (Proof shortened by Zhi Wang, 19-Sep-2024)

	Ref	Expression
Assertion	2oex	$$⊢2_{𝑜}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		df2o3	$$⊢2_{𝑜}=\left\{\varnothing ,1_{𝑜}\right\}$$
2		prex	$$⊢\left\{\varnothing ,1_{𝑜}\right\}\in \mathrm{V}$$
3	1 2	eqeltri	$$⊢2_{𝑜}\in \mathrm{V}$$