Theorem imaeq12d

Description: Equality theorem for image. (Contributed by Mario Carneiro, 4-Dec-2016)

	Ref	Expression
Hypotheses	imaeq1d.1	|- ( ph -> A = B )
	imaeq12d.2	|- ( ph -> C = D )
Assertion	imaeq12d	|- ( ph -> ( A " C ) = ( B " D ) )

Proof

Step	Hyp	Ref	Expression
1		imaeq1d.1	|- ( ph -> A = B )
2		imaeq12d.2	|- ( ph -> C = D )
3	1	imaeq1d	|- ( ph -> ( A " C ) = ( B " C ) )
4	2	imaeq2d	|- ( ph -> ( B " C ) = ( B " D ) )
5	3 4	eqtrd	|- ( ph -> ( A " C ) = ( B " D ) )