Let $M$ be a finite matroid with ground set $E(M)$, and let $e,f \in E(M)$ satisfy $e \ne f$. Adopt the convention that, whenever an element $g$ is a loop in the matroid in which it is to be contracted, the contraction by $g$ is defined to be deletion by $g$.
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Then the following matroids have the common ground set $E(M)\setminus\{e,f\}$ and are equal under the identity map on that ground set:
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\begin{align*}
(M\setminus e)\setminus f = (M\setminus f)\setminus e.
\end{align*}
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Also,
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\begin{align*}
(M/e)/f = (M/f)/e.
\end{align*}
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Finally,
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\begin{align*}
(M\setminus e)/f = (M/f)\setminus e.
\end{align*}
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Consequently, if $N$ is a minor of $M$ obtained by a finite sequence of deletions and contractions, then there exist disjoint subsets $C,D \subset E(M)$ such that
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\begin{align*}
N = M/C \setminus D,
\end{align*}
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and the resulting matroid is independent of the order in which the individual deletions of elements of $D$ and contractions of elements of $C$ are performed.