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Metamath Proof Explorer

Theorem funfn

Description: A class is a function if and only if it is a function on its domain. (Contributed by NM, 13-Aug-2004)

		Ref	Expression
	Assertion	funfn	$⊢ Fun A \leftrightarrow A Fn dom A$

Step	Hyp	Ref	Expression
1		eqid	$⊢ dom A = dom A$
2	1	biantru	$⊢ Fun A \leftrightarrow (Fun A \land dom A = dom A)$
3		df-fn	$⊢ A Fn dom A \leftrightarrow (Fun A \land dom A = dom A)$
4	2 3	bitr4i	$⊢ Fun A \leftrightarrow A Fn dom A$