Theorem finonex

Description: The finite ordinals are a set. See also onprc and fiprc for proof that On and Fin are proper classes. (Contributed by RP, 27-Sep-2023)

	Ref	Expression
Assertion	finonex	$$⊢\mathrm{On}\cap \mathrm{Fin}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		onfin2	$$⊢\mathrm{\omega }=\mathrm{On}\cap \mathrm{Fin}$$
2		omex	$$⊢\mathrm{\omega }\in \mathrm{V}$$
3	1 2	eqeltrri	$$⊢\mathrm{On}\cap \mathrm{Fin}\in \mathrm{V}$$