Theorem breq2dd

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

	Ref	Expression
Hypotheses	breq2dd.1	$$⊢\phi \to A=B$$
	breq2dd.2	$$⊢\phi \to CRA$$
Assertion	breq2dd	$$⊢\phi \to CRB$$

Proof

Step	Hyp	Ref	Expression
1		breq2dd.1	$$⊢\phi \to A=B$$
2		breq2dd.2	$$⊢\phi \to CRA$$
3	1	breq2d	$$⊢\phi \to \left(CRA\leftrightarrow CRB\right)$$
4	2 3	mpbid	$$⊢\phi \to CRB$$