Theorem breq2

Description: Equality theorem for a binary relation. (Contributed by NM, 31-Dec-1993)

	Ref	Expression
Assertion	breq2	$$⊢A=B\to \left(CRA\leftrightarrow CRB\right)$$

Proof

Step	Hyp	Ref	Expression
1		opeq2	$$⊢A=B\to ⟨C,A⟩=⟨C,B⟩$$
2	1	eleq1d	$$⊢A=B\to \left(⟨C,A⟩\in R\leftrightarrow ⟨C,B⟩\in R\right)$$
3		df-br	$$⊢CRA\leftrightarrow ⟨C,A⟩\in R$$
4		df-br	$$⊢CRB\leftrightarrow ⟨C,B⟩\in R$$
5	2 3 4	3bitr4g	$$⊢A=B\to \left(CRA\leftrightarrow CRB\right)$$