Am I correct in assuming:
using A-B = AnB'
(A-B)-C = (A-C)-B
(AnB') - C
(AnB')nC'
AnB'nC'
AnC'nB' <- is this legal?
(A-C)nB'
= (A-C)-B
Thanks for any help.
Yes, that's legal because $\displaystyle \cap$ is commutative ($\displaystyle A\cap B=B\cap A$) and associative ($\displaystyle (A\cap B)\cap C=A\cap(B\cap C)$).
Thus, you're correct in saying that
$\displaystyle \begin{aligned}A\cap B^{\prime}\cap C^{\prime}&=A\cap(B^{\prime}\cap C^{\prime})\\ &= A\cap(C^{\prime}\cap B^{\prime})\\ &=(A\cap C^{\prime})\cap B^{\prime}\end{aligned}$
from which the desired result follows.
Does this make sense?