Metamath Proof Explorer

Theorem 3brtr4d

Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 21-Feb-2005)

Ref Expression
Hypotheses 3brtr4d.1 φ A R B
3brtr4d.2 φ C = A
3brtr4d.3 φ D = B
Assertion 3brtr4d φ C R D


Step Hyp Ref Expression
1 3brtr4d.1 φ A R B
2 3brtr4d.2 φ C = A
3 3brtr4d.3 φ D = B
4 2 3 breq12d φ C R D A R B
5 1 4 mpbird φ C R D