If $f_m$ is a sequence of continuous functions which converges to a function. then that function if continuous as well.

I was looking for the proof is this theorem, but I couldn’t find it anywhere.

the theorem is stated formally:

If $ f_m$ is a sequence of continuous functions defined on $ D$ (subset of $ R$ ) such that $ f_m$ $ \to$ $ f$ uniformly on $ D$ then $ f$ is continous.