Consider the polynomial ring $R = k[x_1, \ldots, x_n]$ in $n$ indeterminates over an algebraically closed field $k$ (my relevant case is the complex numbers). Furthermore, consider an algebraic variety V in the affine space $k^n$, whose associated polynomial ideal we label as $I$ [we note that I is radical]. Finally, define $R_V = R/I$, that is the quotient ring of $R$ by $I$ -- the coordinate ring of the variety $V$.

In this question, it is stated that if $I$ is generated by m elements and $\mathrm{codim}(I) = m$, (i.e. $I$ is generated by a regular sequence), then (for a Cohen-Macaulay ring such as $R$) $R/I$ is also Cohen-Macaulay.

I can easily find a reference for this fact if $R$ is a local Cohen-Macaulay ring. However, I am unable to find a reference in the case that $R$ is only Cohen-Macaulay (such as the polynomial ring in question). If my understanding is correct, can anyone provide a reference for this fact (potentially alongside a proof)?