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;
reserve e for object, X,X1,X2,Y1,Y2 for set;

theorem
 B = [x,{x}] implies B in [:{x},B:]
  proof assume
A1:  B = [x,{x}];
    then [:{x},B:] = { [x,{x}], [x,{x,{x}}] } by Th29;
   hence thesis by TARSKI:def 2,A1;
  end;
