Theorem dfrn4

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

	Ref	Expression
Assertion	dfrn4	⊢ ran 𝐴 = ( 𝐴 “ V )

Proof

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 )