Math help please! Prove (A - B) - C ⊆ (A - C)

Here's the q, thanks everyone!

let A, B, C be sets, (A - B) - C ⊆ (A - C)

prove this without using venn diagrams.

Cheers!

Suppose x is in (A - B) - C. Then x is in A - B and x is not in C. But x in A - B says x is in A and x is not in B. Thus x is in A and x is not in C, so x is in A - C. Therefore, (A - B) - C is a subset of (A - C).