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Metamath Proof Explorer

Theorem 3brtr3g

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

Ref Expression
Hypotheses 3brtr3g.1 
|- ( ph -> A R B )
3brtr3g.2 
|- A = C
3brtr3g.3 
|- B = D
Assertion 3brtr3g 
|- ( ph -> C R D )

Proof

Step Hyp Ref Expression
1 3brtr3g.1 
 |-  ( ph -> A R B )
2 3brtr3g.2 
 |-  A = C
3 3brtr3g.3 
 |-  B = D
4 2 3 breq12i 
 |-  ( A R B <-> C R D )
5 1 4 sylib 
 |-  ( ph -> C R D )