theorem Th53:
  G is commutative Group implies H is commutative
proof
  assume
A1: G is commutative Group;
  thus for h1,h2 holds h1 * h2 = h2 * h1
  proof
    let h1,h2;
    reconsider g1 = h1, g2 = h2 as Element of G by Th42;
    thus h1 * h2 = g1 * g2 by Th43
      .= g2 * g1 by A1,Lm2
      .= h2 * h1 by Th43;
  end;
end;
