
theorem Th20: :: Center2:
  for R being finite Skew-Field holds 1 < card (the carrier of center R)
proof
  let R be finite Skew-Field;
A1: card {0.R, 1.R} = 2 by CARD_2:57;
  0.R in center R by Th18;
  then
A2: 0.R in the carrier of center R;
  for s being Element of R holds (1.R)*s = s*(1.R);
  then 1.R in center R by Th17;
  then 1.R in the carrier of center R;
  then {0.R, 1.R} c= the carrier of center R by A2,ZFMISC_1:32;
  then 2 <= card the carrier of center R by A1,NAT_1:43;
  hence thesis by XXREAL_0:2;
end;
