[Tex/LaTex] tikz: how to place a node aligned with two other nodes

Question

Having seen this answer How to position tikz node relative to 2 other nodes, I thought I'd try something similar, but must be missing a step.

Here is my code

\documentclass[tikz,border=5mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning}
\begin{document}

\begin{tikzpicture}
    \node (A) {A};
    \node [right = of A] (B) {B};
    \node [right = of B] (C) {C};
    \node [below = of A] (D) {D};
    \node [right = of D -| C] (E) {E};
    \node [below = of C |- D] (F) {F};
\end{tikzpicture}

\end{document}

I'd like to position node E to the right of node D and under node C, but I seem to get one but not the other. Why?

Answer 1

The perpendicular coordinate system helps. The node is placed on the base line of node D and in the horizontal middle of node C:

\documentclass[tikz,border=5mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning}
\begin{document}

\begin{tikzpicture}
    \node (A) {A};
    \node [right = of A] (B) {B};
    \node [right = of B] (C) {C};
    \node [below = of A] (D) {D};
    \node [anchor=base] (E) at (C |- D.base) {E};
\end{tikzpicture}

\end{document}

Vertical centering is even easier:

\node (E) at (C |- D) {E};