Proof that $\nabla \cdot (A \times B) = (\nabla \times A) \cdot B - A \cdot (\nabla \times B) $

Question

What is the proof that for two vector fields $A, B : \mathbb R^3 \rightarrow \mathbb R^3$, $$\nabla \cdot (A \times B) = (\nabla \times A) \cdot B - A \cdot (\nabla \times B)$$