This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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 ) )