Curl of Vector Field is Solenoidal

Theorem
Let $\map {\R^3} {x, y, z}$ denote the real Cartesian space of $3$ dimensions.

Let $\mathbf V$ be a vector field on $\R^3$:

Then the curl of $\mathbf V$ is a solenoidal vector field.

Proof
By definition, a solenoidal vector field is one whose divergence is zero.

The result follows from Divergence of Curl is Zero.