Theorem imaeq2

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

	Ref	Expression
Assertion	imaeq2	|- ( A = B -> ( C " A ) = ( C " B ) )

Proof

Step	Hyp	Ref	Expression
1		reseq2	|- ( A = B -> ( C |` A ) = ( C |` B ) )
2	1	rneqd	|- ( A = B -> ran ( C |` A ) = ran ( C |` B ) )
3		df-ima	|- ( C " A ) = ran ( C |` A )
4		df-ima	|- ( C " B ) = ran ( C |` B )
5	2 3 4	3eqtr4g	|- ( A = B -> ( C " A ) = ( C " B ) )