6.5 The fundamental theorem of homomorphism for groups 46.5.1.Homomorphism kernel and homomorphism image t Lemma 4: Let G; *I and IG; l be groups, and op be a homomorphism function from G to G. Then pleg) is identity element of IG;. that x=p(aP(GEG. Then 3 aEG such ◆ Proof:Letx6.5 The fundamental theorem of homomorphism for groups 6.5.1.Homomorphism kernel and homomorphism image  Lemma 4: Let [G;*] and [G';•] be groups, and  be a homomorphism function from G to G'. Then (eG) is identity element of [G';•].  Proof: Let x(G)G'. Then  aG such that x=(a)