Metamath Proof Explorer

Theorem oteq3d

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

Ref Expression
Hypothesis oteq1d.1 
|- ( ph -> A = B )
Assertion oteq3d 
|- ( ph -> <. C , D , A >. = <. C , D , B >. )

Proof

Step Hyp Ref Expression
1 oteq1d.1 
 |-  ( ph -> A = B )
2 oteq3 
 |-  ( A = B -> <. C , D , A >. = <. C , D , B >. )
3 1 2 syl 
 |-  ( ph -> <. C , D , A >. = <. C , D , B >. )