Verified answer

Let x,y∈∩Hi ⇒ x,y∈Hi ∀i ⇒y^-1∈Hi ∀i (Hi is a subgroup ∀i) ⇒xy^-1∈Hi ∀i (Hi is a subgroup ∀i) ⇒xy^-1∈∩Hi ⇒ ∩Hi is a subgroup