Theorem breqan12rd

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

	Ref	Expression
Hypotheses	breq1d.1	$$⊢\phi \to A=B$$
	breqan12i.2	$$⊢\psi \to C=D$$
Assertion	breqan12rd	$$⊢\left(\psi \wedge \phi \right)\to \left(ARC\leftrightarrow BRD\right)$$

Proof

Step	Hyp	Ref	Expression
1		breq1d.1	$$⊢\phi \to A=B$$
2		breqan12i.2	$$⊢\psi \to C=D$$
3	1 2	breqan12d	$$⊢\left(\phi \wedge \psi \right)\to \left(ARC\leftrightarrow BRD\right)$$
4	3	ancoms	$$⊢\left(\psi \wedge \phi \right)\to \left(ARC\leftrightarrow BRD\right)$$