Theorem breqd

Description: Equality deduction for a binary relation. (Contributed by NM, 29-Oct-2011)

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

Proof

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