How to write following equation

Question

I am trying to write the following equation for my paper. I am familiar with using big braces, but I am not sure how to write multiple lines within the braces as in the image attached. The following gives me the left side and the huge braces:

$t\rightarrow_{A}t' \iff \Bigg\{ \exists C$

Answer 1

Summarising everything (had some free-time) ;-).

\documentclass[10pt,a4paper]{article}
\usepackage{amsmath}
\begin{document}
$   t\xrightarrow[\mathcal{A}]{} t'\Leftrightarrow\begin{cases}
\exists C\in\mathcal{C}(\mathcal{F}\cup Q),\exists u_1,\ldots,u_n\in T(\mathcal{F}),\\
\exists f(q_1(x_1),\ldots,q_n(x_n))\rightarrow q(f(x_1,\ldots,x_n))\in\Delta,\\
t=C[f(q_1(u_1),\ldots,q_n(u_n))],\\
t'=C[q(f(u_1,\ldots,u_n))].
\end{cases}$        
\end{document}

you will get:

Answer 2

Summarizing the above comments, you can try

\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
a \iff b \iff
\begin{cases}
c = d\\
e = f
\end{cases}
\end{equation*}
\end{document}