Let $\mathcal{O}$ be an open subset of the plane $\mathbb{R}^{2}$ and let the mapping $F : \mathcal{O} \rightarrow \mathbb{R}^{2}$ be represented by $F(x, y) = (u(x, y), v(x, y))$ for $(x, y)$ in $\mathcal{O}$. Then, we say the mapping $F : \mathcal{O} \rightarrow \mathbb{R}^{2}$ is called a Cauchy-Riemann mapping provided that each of the functions $u : \mathcal{O} \rightarrow \mathbb{R}$ and $v : \mathcal{O} \rightarrow \mathbb{R}$ has continuous second-order partial derivatives and $$\frac{\partial u}{\partial x}(x, y) = \frac{\partial v}{\partial y}(x, y) \hspace{1em} \text{ and } \hspace{1em} \frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x}(x, y)$$
for all $(x, y)$ in $\mathcal{O}$.
Prove that if $w : \mathbb{R}^{2} \rightarrow \mathbb{R}$ is harmonic and the mapping $F : \mathcal{O} \rightarrow \mathbb{R}^{2}$ is a Cauchy-Riemann mapping, then the function $w \circ F : \mathcal{O} \rightarrow \mathbb{R}$ is also harmonic.
So I know that a function is harmonic provided that the sum of its second derivatives equals $0$. This means we have $\nabla^2 w = 0$.
Also, we can write $F(x, y) = (u(x, y), v(x,y))$. I don't really know how to prove this fact. We have the relations above in the definition of a Cauchy-Riemann mapping, but I'm not so sure about where to use them.
I would appreciate some help.