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 Th56:
  X \ {x} = X iff not x in X
proof
  X \ {x} = X iff X misses {x} by XBOOLE_1:83;
  hence thesis by Lm5,Lm6;
end;
