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	|- ( On i^i Fin ) e. _V

Proof

Step	Hyp	Ref	Expression
1		onfin2	|- _om = ( On i^i Fin )
2		omex	|- _om e. _V
3	1 2	eqeltrri	|- ( On i^i Fin ) e. _V