theorem
  for H being Group st G,H are_isomorphic & G is commutative
  holds H is commutative
proof
  let H be Group;
  assume that
A1: G,H are_isomorphic and
A2: G is commutative;
  consider h being Homomorphism of G,H such that
A3: h is bijective by A1;
  now
    let c,d be Element of H;
    consider a such that
A4: h.a = c by A3,Th58;
    consider b such that
A5: h.b = d by A3,Th58;
    thus c * d = h.(a * b) by A4,A5,Def6
      .= h.(b * a) by A2
      .= d * c by A4,A5,Def6;
  end;
  hence thesis;
end;
