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Metamath Proof Explorer

Theorem breqtrrd

Description: Substitution of equal classes into a binary relation. (Contributed by NM, 24-Oct-1999)

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

Proof

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