This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem fnima

Description: The image of a function's domain is its range. (Contributed by NM, 4-Nov-2004) (Proof shortened by Andrew Salmon, 17-Sep-2011)

		Ref	Expression
	Assertion	fnima	$⊢ F Fn A \to F [A] = ran F$

Step	Hyp	Ref	Expression
1		df-ima	$⊢ F [A] = ran ({F ↾}_{A})$
2		fnresdm	$⊢ F Fn A \to {F ↾}_{A} = F$
3	2	rneqd	$⊢ F Fn A \to ran ({F ↾}_{A}) = ran F$
4	1 3	eqtrid	$⊢ F Fn A \to F [A] = ran F$