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

Metamath Proof Explorer

Theorem oteq1d

Description: Equality deduction for ordered triples. (Contributed by Mario Carneiro, 11-Jan-2017)

Ref Expression
Hypothesis oteq1d.1 
|- ( ph -> A = B )
Assertion oteq1d 
|- ( ph -> <. A , C , D >. = <. B , C , D >. )

Proof

Step Hyp Ref Expression
1 oteq1d.1 
 |-  ( ph -> A = B )
2 oteq1 
 |-  ( A = B -> <. A , C , D >. = <. B , C , D >. )
3 1 2 syl 
 |-  ( ph -> <. A , C , D >. = <. B , C , D >. )