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Metamath Proof Explorer

Theorem breqtrrdi

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

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

Proof

Step Hyp Ref Expression
1 breqtrrdi.1 
 |-  ( ph -> A R B )
2 breqtrrdi.2 
 |-  C = B
3 2 eqcomi 
 |-  B = C
4 1 3 breqtrdi 
 |-  ( ph -> A R C )