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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