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Metamath Proof Explorer

Theorem eqbrtrrd

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

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

Proof

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