Theorem breq12

Description: Equality theorem for a binary relation. (Contributed by NM, 8-Feb-1996)

	Ref	Expression
Assertion	breq12	$$⊢\left(A=B\wedge C=D\right)\to \left(ARC\leftrightarrow BRD\right)$$

Proof

Step	Hyp	Ref	Expression
1		breq1	$$⊢A=B\to \left(ARC\leftrightarrow BRC\right)$$
2		breq2	$$⊢C=D\to \left(BRC\leftrightarrow BRD\right)$$
3	1 2	sylan9bb	$$⊢\left(A=B\wedge C=D\right)\to \left(ARC\leftrightarrow BRD\right)$$