Proof: Intersection of Subgroups is a Subgroup of H in G

[playa007]

Homework Statement

If H, K are subgroups of G, show that H intersect K is a subgroup of H

Homework Equations

I know that H intersect K is a subgroup of G; I proved this already but I'm wondering how H intersect K is a subgroup of H

The Attempt at a Solution

I'm quite sure this is true but my idea is based on set theoretic properties and one can't use such properties to apply on subgroups

 

[Dick]

If you've proved H intersect K is a group, then there is nothing more to prove. H intersect K is contained H and it's a group. Therefore it's a subgroup of H. That's the definition of 'subgroup'.