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

theorem Th9:
  for a being Function of Y,BOOLEAN holds a 'or' I_el(Y)= I_el(Y)
proof
  let a be Function of Y,BOOLEAN;
  let x be Element of Y;
  thus (a 'or' I_el(Y)).x = a.x 'or' I_el(Y).x by Def4
     .= a.x 'or' TRUE by Def11
     .= I_el(Y).x by Def11;
end;
