How to prove the isomorphism $ \mathcal{O}_{X,c} \cong \mathcal{O}_{V,c} / I_{V}(X) \mathcal{O}_{V,c} $ [closed]

If $V$ is an affine variety and $X, Y \subsetneq V$ are pure dimensional and closed, and $c$ is a zero dimensional irreducible component of $X \cap Y$.

Then how to prove $ \mathcal{O}_{X,c} \cong \mathcal{O}_{V,c} / I_{V}(X) \mathcal{O}_{V,c} $ ?

I honestly have no idea how to approach this question after thinking about it, I think I'm missing a fundamental point here. I greatly appreciate any tips.