Using Regular Value Theorem to Show that $S^2$ is a $2$-dimensional Manifold.

Question

If we let $F(x,y,z) = x^2+y^2+z^2-1$. Then we know that $DF = (2x,2y,2z)$. I am confused as to how I should show that $0$ is a regular value of this function. I think I am missing something very simple. Is it enough to just say that at all of the points for which $F$ is $0$, $DF$ has rank $1$? This would imply that we have a 2-dimensional manifold.