Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that

(i)	$E, F \in \mathcal{F}$ are each a D1109: Measurable set in $M$
(ii)	$E \subseteq F$ is a D78: Subset of $F$
(iii)	\begin{equation} \mu(E) < \infty \end{equation}

By definition, $E \triangle F : = (E \setminus F) \cup (F \setminus E)$. Since $E \setminus F$ and $F \setminus E$ are disjoint and since $E$ is contained in $F$ with the measure of $E$ finite, we may use results

(i)	R976: Finite disjoint additivity of unsigned basic measure
(ii)	R4444: Superset differenced from set equals empty set
(iii)	R978: Measure of set difference

to obtain \begin{equation} \begin{split} \mu(E \triangle F) = \mu(E \setminus F) + \mu(F \setminus E) = \mu(\emptyset) + \mu(F) - \mu(E) = \mu(F) - \mu(E) \end{split} \end{equation} $\square$