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Metamath Proof Explorer

Theorem breqtrrid

Description: A chained equality inference for a binary relation. (Contributed by NM, 24-Apr-2005)

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

Proof

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