Math Help - Set Proof

1. Set Proof

THM: $(A-B) - C = (A-C) - (B -C)\ \ \forall$ sets $A,B,C$.

Prove the above thm.

2. $\begin{array}{l}
\left( {A \cap C^c } \right) \cap \left( {B \cap C^c } \right)^c \\
\left( {A \cap C^c } \right) \cap \left( {B^c \cup C} \right) \\
\left( {A \cap C^c \cap B^c } \right) \\
\end{array}
$

3. Originally Posted by Plato
$\begin{array}{l}
\left( {A \cap C^c } \right) \cap \left( {B \cap C^c } \right)^c \\
\left( {A \cap C^c } \right) \cap \left( {B^c \cup C} \right) \\
\left( {A \cap C^c \cap B^c } \right) \\
\end{array}
$
I appreciate it. I believe the $C^c$ for instance means the compliment of C (that is everything that is not C)- is there another way to prove this? I don't quite see how it proves it. Thanks for the explanation.

4. $\left( {A \cap C^c \cap B^c } \right) = \left( {A \cap B^c } \right) \cap C^c = \left( {A\backslash B} \right)\backslash C
$