theorem Th53:
  G is Abelian addGroup implies H is Abelian
proof
  assume
A1: G is Abelian addGroup;
  thus for h1,h2 holds h1 + h2 = h2 + h1
  proof
    let h1,h2;
    reconsider g1 = h1, g2 = h2 as Element of G by Th41,STRUCT_0:def 5;
    thus h1 + h2 = g1 + g2 by Th43
      .= g2 + g1 by A1,Lm2
      .= h2 + h1 by Th43;
  end;
end;
