What environment to use in writing formal deductions?

Question

Learning about mathematical logic, I have to write formal deductions*.

How can I write them using TeX?

Any feedback is welcome.

---

(*)Roughly they are numbered lists over two columns, the first one gives a formula and the second one gives its justification (if it is an axiom, a hypothesis or if it is inferred by previous entries), both can go over many rows.
Anyway here is an example (from: Mendelson, Intro. to Math. Logic.)

Answer 1

Here is one way to do it using a custom counter for the first column, and the p{} column types for the other two columns:

Code:

\documentclass{article}
\usepackage{amssymb}

\newcounter{MyRowNumber}
\newcommand*{\NewRow}{\stepcounter{MyRowNumber}\arabic{MyRowNumber}}%

\begin{document}
\begin{tabular}{l p{0.25\linewidth} p{0.25\linewidth}}
    \NewRow & $x^2 + y^2 \ge 0\ \forall x, y \in \mathbb{R}$ & Hyp\\
    \NewRow & $more\ math$                                   & 10,11 conjunction introduction\\
\end{tabular}
\end{document}