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
 not A in [:A,B:]
  proof
   assume A in [:A,B:];
    then consider x,y being object such that
A1:   x in A & y in B & A = [x,y] by Th83;
    reconsider x as set by TARSKI:1;
    x = {x} or x = {x,y} by A1,TARSKI:def 2;
    then x in x by TARSKI:def 1,def 2;
   hence contradiction;
  end;
