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 Th130:
 X is non empty trivial implies ex x st X = {x}
 proof
  assume X is non empty;
   then consider x being object such that
A1:  x in X;
  assume
A2:  X is trivial;
  take x;
  for y being object holds y in X iff x = y by A2,A1;
  hence thesis by TARSKI:def 1;
 end;
