Metamath Proof Explorer

Theorem 3brtr3i

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

Ref Expression
Hypotheses 3brtr3.1 
|- A R B
3brtr3.2 
|- A = C
3brtr3.3 
|- B = D
Assertion 3brtr3i 
|- C R D

Proof

Step Hyp Ref Expression
1 3brtr3.1 
 |-  A R B
2 3brtr3.2 
 |-  A = C
3 3brtr3.3 
 |-  B = D
4 2 1 eqbrtrri 
 |-  C R B
5 4 3 breqtri 
 |-  C R D