How the first two steps of the theorem came?

me properties of 198| Theoremn: Every subgroup of an abelian group is a normal group. p Proof. Let H be a subgroup of any commutative group G. xeGand h e H, then xhx= (hx)x G i = hxx) by as = he = h eH Thus, x E GheHxhx e H, His a normal subgroup of G. roun