Consider the following pushout diagram
$\require{AMScd}$
\begin{CD}
A @>f>> B\\
@V g V V @VV  V\\
C @>> > D
\end{CD}
in the category of $\textbf{Rings}$ where $f,g$ both are flat monomorphisms. The diagram is also a pullback diagram. 

I'm trying to prove it but could not.