# Is there a better way to align the parts of this proof?

Is there a better way to align the parts of this proof.

\documentclass{article}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}
\begin{document}
Notice that
\begin{align*}
(a_{0}, b_{0}) \equiv (a_{1}, b_{1}) &\hspace{4pt} \text{iff} \quad \text{definition of } \equiv \\
\begin{aligned} a_{0} \neg (a_{0} \wedge b_{0}) &= a_{1} \neg (a_{1} \wedge b_{1}) \text{ and } \\
b_{0} \neg (a_{0} \wedge b_{0}) &= b_{1} \neg (a_{0} \wedge b_{0}) \end{aligned} \bigg\} &\hspace{4pt} \text{iff} \quad \text{using proposition 11.1} \\
\begin{aligned} a_{0} \wedge b_{0}^\prime &= a_{1} \wedge b_{1}^\prime \text{ and } \\ b_{0} \wedge a_{0}^\prime &= b_{1} \wedge a_{1}^\prime \end{aligned} \bigg\} &\hspace{4pt} \text{.}
\end{align*}
The first statement holds.
\end{document}

• You could try something like structured derivations, making the iff left-aligned, a hint why in parentheses or braces, etc. Commented Nov 19, 2021 at 14:38
• @Alex Nelson By writing a statement on the left and a reason for the next line on the right, readers who are familiar with the material can just read the left column. The right braces indicate the two lines are parts of one statement. Sometimes the reasons require two lines which are joined by a left brace.
– Jay
Commented Nov 19, 2021 at 16:55