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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 ) ∈ On

Proof

Step	Hyp	Ref	Expression
1		harf	⊢ har : V ⟶ On
2		0elon	⊢ ∅ ∈ On
3	1 2	f0cli	⊢ ( har ‘ 𝑋 ) ∈ On