\documentclass{amsart}
\usepackage{tikz-cd}
\begin{document}
\begin{tikzpicture}[baseline= (a).base][>=stealth,>=implies]
\node[scale=1.4] (a) at (0,0){
\begin{tikzcd}
\text{(a)} \rar[Leftrightarrow]
& [1.8em] \text{(b)}
& [2em] \text{(c)}\lar[Leftarrow]\arrow[ddl,Rightarrow]\footnotesize\text{(i,ii, or iii)}\\
& \vspace{-5mm} \\&\text{\hspace{1mm}(b)$^\prime$}\arrow[uu,Leftrightarrow]
\end{tikzcd}
};
\end{tikzpicture}
\end{document}
Questions:
(1) How can I make the diagonal arrow start at (c), as it normally would without "(i,ii, or iii)"?
(2) The arrow from (b) to (c) needs a line through the center, similar to what $\centernot\implies$ produces:




& \hspace{-3em}before of "(i,ii, or iii)" – Fran May 31 '17 at 06:36\arrow[ddl,Rightarrow,start anchor=south west]is better. (I'm working on the second point). – CarLaTeX May 31 '17 at 06:52