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Metamath Proof Explorer

Theorem dfrn4

Description: Range defined in terms of image. (Contributed by NM, 14-May-2008)

		Ref	Expression
	Assertion	dfrn4	$⊢ ran A = A [V]$

Step	Hyp	Ref	Expression
1		df-ima	$⊢ A [V] = ran ({A ↾}_{V})$
2		rnresv	$⊢ ran ({A ↾}_{V}) = ran A$
3	1 2	eqtr2i	$⊢ ran A = A [V]$