Theorem resima

Description: A restriction to an image. (Contributed by NM, 29-Sep-2004)

	Ref	Expression
Assertion	resima	|- ( ( A |` B ) " B ) = ( A " B )

Proof

Step	Hyp	Ref	Expression
1		residm	|- ( ( A |` B ) |` B ) = ( A |` B )
2	1	rneqi	|- ran ( ( A |` B ) |` B ) = ran ( A |` B )
3		df-ima	|- ( ( A |` B ) " B ) = ran ( ( A |` B ) |` B )
4		df-ima	|- ( A " B ) = ran ( A |` B )
5	2 3 4	3eqtr4i	|- ( ( A |` B ) " B ) = ( A " B )