
theorem Th17:
  for R being Skew-Field holds 1_R = 1_MultGroup R
proof
  let R be Skew-Field;
A1: the carrier of MultGroup R = NonZero R by Def1;
  not 1_R in {0.R} by TARSKI:def 1;
  then reconsider uR = 1_R as Element of MultGroup R by A1,XBOOLE_0:def 5;
  now
    let h be Element of MultGroup R;
    reconsider g = h as Element of R by A1,XBOOLE_0:def 5;
    g * 1_R = g;
    hence h * uR = h by Th16;
    1_R * g = g;
    hence uR * h = h by Th16;
  end;
  hence thesis by GROUP_1:def 4;
end;
