集合A属于B,证明A和B的交集为A

for all x ∈ A∩B
=> x ∈ A and x ∈B
=> x ∈ A ( A is subset of B)
=> A∩B is subset of A --(1)
and
for all x ∈ A
=> x ∈ A and x ∈ B ( A is subset of B)
=> x ∈ A∩B
=> A is subset of A∩B ---(2)
from (1),(2),we have
A= A∩B