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Metamath Proof Explorer

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	$⊢ rank (A) \in On$

Proof

Step	Hyp	Ref	Expression
1		rankf	$⊢ rank : ⋃ R_{1} [On] ⟶ On$
2		0elon	$⊢ \emptyset \in On$
3	1 2	f0cli	$⊢ rank (A) \in On$