Theorem breq1dd

Description: Equality deduction for a binary relation. (Contributed by Thierry Arnoux, 10-Jan-2026)

	Ref	Expression
Hypotheses	breq1dd.1	$$⊢\phi \to A=B$$
	breq1dd.2	$$⊢\phi \to ARC$$
Assertion	breq1dd	$$⊢\phi \to BRC$$

Proof

Step	Hyp	Ref	Expression
1		breq1dd.1	$$⊢\phi \to A=B$$
2		breq1dd.2	$$⊢\phi \to ARC$$
3	1	breq1d	$$⊢\phi \to \left(ARC\leftrightarrow BRC\right)$$
4	2 3	mpbid	$$⊢\phi \to BRC$$