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
  X \/ {x} c= Y iff x in Y & X c= Y
proof
 X c= Y & {x} c= Y implies X \/ {x} c= Y by XBOOLE_1:8;
  hence thesis by Lm1,XBOOLE_1:11;
end;
