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Metamath Proof Explorer

Theorem harf

Description: Functionality of the Hartogs function. (Contributed by Stefan O'Rear, 11-Feb-2015)

		Ref	Expression
	Assertion	harf	$⊢ har : V ⟶ On$

Step	Hyp	Ref	Expression
1		df-har	$⊢ har = (x \in V ⟼ \{y \in On \| y ≼ x\})$
2		hartogs	$⊢ x \in V \to \{y \in On \| y ≼ x\} \in On$
3	1 2	fmpti	$⊢ har : V ⟶ On$