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 x in X implies (X\/{x})\{x}=X
proof
A1: (X \/ {x}) \ {x} = X \ {x} by XBOOLE_1:40;
  assume not x in X;
  hence thesis by A1,Th56;
end;
