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\setlength\subproofhorizspace{1em}
\begin{logicproof}{0}
x = g(y) & prem.\\
f(g(y)) = z & prem.\\
f(x) = y & prem.\\
f(x) = z & $= \mathrm{e}$ 2,1\\
y = z & $= \mathrm{e}$ 4,3
\end{logicproof}