reserve X,X1,X2,Y,Y1,Y2 for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,g1,g2,h for Function,
  R,S for Relation;
reserve e,u for object,
  A for Subset of X;

theorem
 X <> {} & X c= dom f implies f.:X <> {}
 proof assume X <> {};
   then ex x being object st x in X by XBOOLE_0:def 1;
  hence thesis by Th107;
 end;
