Theorem reseq1d

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

	Ref	Expression
Hypothesis	reseqd.1	|- ( ph -> A = B )
Assertion	reseq1d	|- ( ph -> ( A |` C ) = ( B |` C ) )

Proof

Step	Hyp	Ref	Expression
1		reseqd.1	|- ( ph -> A = B )
2		reseq1	|- ( A = B -> ( A |` C ) = ( B |` C ) )
3	1 2	syl	|- ( ph -> ( A |` C ) = ( B |` C ) )