Theorem dffn2

Description: Any function is a mapping into _V . (Contributed by NM, 31-Oct-1995) (Proof shortened by Andrew Salmon, 17-Sep-2011)

	Ref	Expression
Assertion	dffn2	$$⊢FFnA\leftrightarrow F:A⟶\mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		ssv	$$⊢\mathrm{ran}F\subseteq \mathrm{V}$$
2	1	biantru	$$⊢FFnA\leftrightarrow \left(FFnA\wedge \mathrm{ran}F\subseteq \mathrm{V}\right)$$
3		df-f	$$⊢F:A⟶\mathrm{V}\leftrightarrow \left(FFnA\wedge \mathrm{ran}F\subseteq \mathrm{V}\right)$$
4	2 3	bitr4i	$$⊢FFnA\leftrightarrow F:A⟶\mathrm{V}$$