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} \/ Z c= Z implies x in Z
proof
  assume
A1: {x,y} \/ Z c= Z;
  assume not x in Z;
  then not x in {x,y} \/ Z by A1;
  then not x in {x,y} by XBOOLE_0:def 3;
  hence thesis by TARSKI:def 2;
end;
