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} = {y1,y2} implies y1 = y2
proof
  assume
A1: { x } = { y1,y2 };
  then x = y1 by Th4;
  hence thesis by A1,Th4;
end;
