
theorem Th3:
   for M be AbGroup
   for f,g be Endomorphism of M holds
   f in Funcs(the carrier of M,the carrier of M) &
   g in Funcs(the carrier of M,the carrier of M) &
   (add_End(M)).[f,g] = (ADD(M,M)).(f,g) &
   (ADD(M,M)).(f,g) is Endomorphism of M
   proof
     let M be AbGroup;
     let f,g be Endomorphism of M;
     f in set_End(M) & g in set_End(M);
     hence thesis by Th2,ZFMISC_1:87,FUNCT_1:49;
   end;
