If $S_n^f(x_0)-S_n^g(x_0)\to 0$, then $f(x_0)=g(x_0)$

Question

Let $f, g\colon [-\pi, \pi]\to\mathbf{R}$ be continuous $2\pi$-periodic functions and let $S_n^f$ and $S_n^g$ be their corresponding partial Fourier sums. I need to show that if $S_n^f(x_0)-S_n^g(x_0)\to 0$, then $f(x_0)=g(x_0)$. The hint to this problem was Fejèr's theorem, but I'm not sure how to proceed. To me this appears to be some kind of opposite result to the Riemann localization principle.