Divergences Of Curls Are Zero

The curl of a vector field V is:

(∂_yV_z - ∂_zV_y, ∂_zV_x - ∂_xV_z, ∂_xV_y - ∂_yV_x).

Its divergence is:

(∂_x∂_yV_z - ∂_x∂_zV_y) + (∂_y∂_zV_x - ∂_y∂_xV_z) + (∂_z∂_xV_y - ∂_z∂_yV_x)

which equals zero.