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Metamath Proof Explorer

Theorem harcl

Description: Values of the Hartogs function are ordinals (closure of the Hartogs function in the ordinals). (Contributed by Stefan O'Rear, 11-Feb-2015)

		Ref	Expression
	Assertion	harcl	$⊢ har (X) \in On$

Proof

Step	Hyp	Ref	Expression
1		harf	$⊢ har : V ⟶ On$
2		0elon	$⊢ \emptyset \in On$
3	1 2	f0cli	$⊢ har (X) \in On$