Show that if A⊆B, then C−B⊆C−A

Let A⊆B
To show: C−B⊆C−A
Let x∈C−B ⇒ x∈C and x∉B ⇒ x∈C and x∉A (A⊆B) ⇒ x∈C−A
∴ C−B⊆C−A