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	$$⊢\mathrm{har}\left(X\right)\in \mathrm{On}$$

Proof

Step	Hyp	Ref	Expression
1		harf	$$⊢\mathrm{har}:\mathrm{V}⟶\mathrm{On}$$
2		0elon	$$⊢\varnothing \in \mathrm{On}$$
3	1 2	f0cli	$$⊢\mathrm{har}\left(X\right)\in \mathrm{On}$$