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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 ⊢ φ → A R B
3brtr4g.2 ⊢ C = A
3brtr4g.3 ⊢ D = B
Assertion 3brtr4g ⊢ φ → C R D

Proof

Step Hyp Ref Expression
1 3brtr4g.1 ⊢ φ → 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 ⊢ φ → C R D