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Metamath Proof Explorer

Theorem breqtrid

Description: A chained equality inference for a binary relation. (Contributed by NM, 11-Oct-1999)

Ref Expression
Hypotheses breqtrid.1 
|- A R B
breqtrid.2 
|- ( ph -> B = C )
Assertion breqtrid 
|- ( ph -> A R C )

Proof

Step Hyp Ref Expression
1 breqtrid.1 
 |-  A R B
2 breqtrid.2 
 |-  ( ph -> B = C )
3 1 a1i 
 |-  ( ph -> A R B )
4 3 2 breqtrd 
 |-  ( ph -> A R C )