We need to show A and B are equal for that we must show A B and B A.

We have s A ϕ (∵ ϕ is a subset of every set)

∴ ϕ A.

Hence A =ϕ.

Suppose A = ϕ

∵ Every set is subset of itself

∴ ϕ = A ϕ

Hence, Proved.