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 <-> A Fn dom A )

Proof

Step	Hyp	Ref	Expression
1		eqid	|- dom A = dom A
2	1	biantru	|- ( Fun A <-> ( Fun A /\ dom A = dom A ) )
3		df-fn	|- ( A Fn dom A <-> ( Fun A /\ dom A = dom A ) )
4	2 3	bitr4i	|- ( Fun A <-> A Fn dom A )