Theorem breqdi

Description: Equality deduction for a binary relation. (Contributed by Thierry Arnoux, 5-Oct-2020)

	Ref	Expression
Hypotheses	breq1d.1	$$⊢\phi \to A=B$$
	breqdi.1	$$⊢\phi \to CAD$$
Assertion	breqdi	$$⊢\phi \to CBD$$

Proof

Step	Hyp	Ref	Expression
1		breq1d.1	$$⊢\phi \to A=B$$
2		breqdi.1	$$⊢\phi \to CAD$$
3	1	breqd	$$⊢\phi \to \left(CAD\leftrightarrow CBD\right)$$
4	2 3	mpbid	$$⊢\phi \to CBD$$