Theorem imaeq1

Description: Equality theorem for image. (Contributed by NM, 14-Aug-1994)

	Ref	Expression
Assertion	imaeq1	|- ( A = B -> ( A " C ) = ( B " C ) )

Proof

Step	Hyp	Ref	Expression
1		reseq1	|- ( A = B -> ( A |` C ) = ( B |` C ) )
2	1	rneqd	|- ( A = B -> ran ( A |` C ) = ran ( B |` C ) )
3		df-ima	|- ( A " C ) = ran ( A |` C )
4		df-ima	|- ( B " C ) = ran ( B |` C )
5	2 3 4	3eqtr4g	|- ( A = B -> ( A " C ) = ( B " C ) )