Let [tex]x\in D\setminus A[/tex], so that [tex]x\in D[/tex] but [tex]x\not\in A[/tex]. Since [tex]D\subset B[/tex], it follows that [tex]x\in B[/tex], and since [tex]C\subset A[/tex], it follows that [tex]x\not\in C[/tex], which means [tex]x\in B\setminus C[/tex].
