reserve u,v,x,x1,x2,y,y1,y2,z,p,a for object,
        A,B,X,X1,X2,X3,X4,Y,Y1,Y2,Z,N,M for set;

theorem
  x <> y implies { x,y } \ { y } = { x }
proof
  assume x <> y;
  then
A1: not x in {y} by TARSKI:def 1;
  y in {y} by TARSKI:def 1;
  hence thesis by A1,Lm11;
end;
