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} /\ X = {x} implies not y in X or x = y
proof
A1: y in {x,y} by TARSKI:def 2;
  assume {x,y} /\ X = {x} & y in X;
  then y in {x} by A1,XBOOLE_0:def 4;
  hence thesis by TARSKI:def 1;
end;
