theorem Th11:
  for G being strict finite Group st card G > 1
  ex a being Element of G st a <> 1_G
proof
  let G be strict finite Group;
  assume that
A1: card G > 1 and
A2: for a being Element of G holds a = 1_G;
  for a being Element of G holds a in (1).G
  proof
    let a be Element of G;
    a = 1_G by A2;
    then a in {1_G} by TARSKI:def 1;
    hence thesis by GROUP_2:def 7;
  end;
  then the multMagma of G = (1).G by GROUP_2:62;
  hence contradiction by A1,GROUP_2:69;
end;
