I basically want to obtain the result (replace Proof -> Solution, and mdframed around the environemnt) simply by the code:
\begin{solution} Set Theory Best Theory. \begin{align*} 2 = \{\emptyset,\{\emptyset\},\{\emptyset,\{\emptyset\}\}\} \end{align*} \end{solution} 
This can be easily done using \renewenvironment. My main issue lies in preserving the optional argument in the proof environment, i.e. something like this would still work:
\begin{solution}[Proof] Set Theory Best Theory. \begin{align*} 2 = \{\emptyset,\{\emptyset\},\{\emptyset,\{\emptyset\}\}\} \end{align*} \end{solution} 
Any help is greatly appreciated.
EDIT: To clarify, I do not have a working solution environment working. The first image above can be made possible by:
\newenvironment{solution} {\begin{mdframed}\begin{proof}[Solution]} {\end{proof}\end{mdframed}} But it will not accept any arguments (so the second image will not be obtained)
solution?