Theorem reseq12d

Description: Equality deduction for restrictions. (Contributed by NM, 21-Oct-2014)

	Ref	Expression
Hypotheses	reseqd.1	|- ( ph -> A = B )
	reseqd.2	|- ( ph -> C = D )
Assertion	reseq12d	|- ( ph -> ( A |` C ) = ( B |` D ) )

Proof

Step	Hyp	Ref	Expression
1		reseqd.1	|- ( ph -> A = B )
2		reseqd.2	|- ( ph -> C = D )
3	1	reseq1d	|- ( ph -> ( A |` C ) = ( B |` C ) )
4	2	reseq2d	|- ( ph -> ( B |` C ) = ( B |` D ) )
5	3 4	eqtrd	|- ( ph -> ( A |` C ) = ( B |` D ) )