let ∅: G → G' be an isomorphism of a group ( G, *) with a group ( G', *'). Write out a proof to convince a skeptic of the intuitively clear statement.

If H is a subgroup of G, then ∅[HJ = {∅(h) | h ∈H} is a subgroup of G'. That is, an isomorphism carries subgroups into subgroups.