Theorem breq1d

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

	Ref	Expression
Hypothesis	breq1d.1	$$⊢\phi \to A=B$$
Assertion	breq1d	$$⊢\phi \to \left(ARC\leftrightarrow BRC\right)$$

Proof

Step	Hyp	Ref	Expression
1		breq1d.1	$$⊢\phi \to A=B$$
2		breq1	$$⊢A=B\to \left(ARC\leftrightarrow BRC\right)$$
3	1 2	syl	$$⊢\phi \to \left(ARC\leftrightarrow BRC\right)$$