
theorem Th16: :: Center0:
  for R being Ring holds the carrier of center R c= the carrier of R
proof
  let R be Ring;
  for x being object st x in the carrier of center R
    holds x in the carrier of R
  proof
    let y be object;
    assume y in the carrier of center R;
    then
    y in {x where x is Element of R: for s being Element of R holds x*s = s*x}
    by Def4;
    then ex x being Element of R st ( x = y)&( for s being Element
    of R holds x*s = s*x);
    hence thesis;
  end;
  hence thesis;
end;
