Metamath Proof Explorer

Theorem 3brtr4i

Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 11-Aug-1999)

Ref Expression
Hypotheses 3brtr4.1 
|- A R B
3brtr4.2 
|- C = A
3brtr4.3 
|- D = B
Assertion 3brtr4i 
|- C R D

Proof

Step Hyp Ref Expression
1 3brtr4.1 
 |-  A R B
2 3brtr4.2 
 |-  C = A
3 3brtr4.3 
 |-  D = B
4 2 1 eqbrtri 
 |-  C R B
5 4 3 breqtrri 
 |-  C R D