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 ∩ Fin ) ∈ V

Proof

Step	Hyp	Ref	Expression
1		onfin2	⊢ ω = ( On ∩ Fin )
2		omex	⊢ ω ∈ V
3	1 2	eqeltrri	⊢ ( On ∩ Fin ) ∈ V