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;
