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	$$⊢\mathrm{rank}\left(A\right)\in \mathrm{On}$$

Proof

Step	Hyp	Ref	Expression
1		rankf	$$⊢\mathrm{rank}:\bigcup R_1\left[\mathrm{On}\right]⟶\mathrm{On}$$
2		0elon	$$⊢\varnothing \in \mathrm{On}$$
3	1 2	f0cli	$$⊢\mathrm{rank}\left(A\right)\in \mathrm{On}$$