Theorem cfon

Description: The cofinality of any set is an ordinal (although it only makes sense when A is an ordinal). (Contributed by Mario Carneiro, 9-Mar-2013)

	Ref	Expression
Assertion	cfon	|- ( cf ` A ) e. On

Proof

Step	Hyp	Ref	Expression
1		cardcf	|- ( card ` ( cf ` A ) ) = ( cf ` A )
2		cardon	|- ( card ` ( cf ` A ) ) e. On
3	1 2	eqeltrri	|- ( cf ` A ) e. On