reserve Y for non empty set;
reserve B for Subset of Y;

theorem Th5:
  for a being Function of Y,BOOLEAN holds a '&' I_el(Y)=a
proof
  let a be Function of Y,BOOLEAN;
  let x be Element of Y;
  thus (a '&' I_el(Y)).x = a.x '&' I_el(Y).x by MARGREL1:def 20
        .= a.x '&' TRUE by Def11
        .= a.x;
end;
