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Metamath Proof Explorer

Theorem 3brtr4g

Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 16-Jan-1997)

Ref Expression
Hypotheses 3brtr4g.1 
|- ( ph -> A R B )
3brtr4g.2 
|- C = A
3brtr4g.3 
|- D = B
Assertion 3brtr4g 
|- ( ph -> C R D )

Proof

Step Hyp Ref Expression
1 3brtr4g.1 
 |-  ( ph -> A R B )
2 3brtr4g.2 
 |-  C = A
3 3brtr4g.3 
 |-  D = B
4 2 3 breq12i 
 |-  ( C R D <-> A R B )
5 1 4 sylibr 
 |-  ( ph -> C R D )