Theorem rankon

Description: The rank of a set is an ordinal number. Proposition 9.15(1) of TakeutiZaring p. 79. (Contributed by NM, 5-Oct-2003) (Revised by Mario Carneiro, 12-Sep-2013)

	Ref	Expression
Assertion	rankon	|- ( rank ` A ) e. On

Proof

Step	Hyp	Ref	Expression
1		rankf	|- rank : U. ( R1 " On ) --> On
2		0elon	|- (/) e. On
3	1 2	f0cli	|- ( rank ` A ) e. On