Metamath Proof Explorer

Theorem dffn3

Description: A function maps to its range. (Contributed by NM, 1-Sep-1999)

		Ref	Expression
	Assertion	dffn3	$⊢ F Fn A \leftrightarrow F : A ⟶ ran F$

Step	Hyp	Ref	Expression
1		ssid	$⊢ ran F \subseteq ran F$
2	1	biantru	$⊢ F Fn A \leftrightarrow (F Fn A \land ran F \subseteq ran F)$
3		df-f	$⊢ F : A ⟶ ran F \leftrightarrow (F Fn A \land ran F \subseteq ran F)$
4	2 3	bitr4i	$⊢ F Fn A \leftrightarrow F : A ⟶ ran F$