Removable singularities of separately harmonic functions

Removable singularities of separately harmonic functions are considered. More precisely, we prove harmonic continuation property of a separately harmonic function $u(x,y)$ in $D\setminus S$ to the domain $D$, when $D\subset\mathbb{R}^n(x)\times\mathbb{R}^m(y)$, $n,m>1$ and $S$ is a closed subset of the domain $D$ with nowhere dense projections $S_1=\{x\in\mathbb{R}^n:(x,y)\in S\}$ and $S_2=\{y\in\mathbb{R}^m:(x,y)\in S\}$.