theorem Th45:
  Funcs({},f) = dom f --> {{}}
proof
A1: now
    let x be object;
    assume x in dom f;
    hence Funcs({},f).x = Funcs({} qua set,f.x) by Def8
      .= {{}} by FUNCT_5:57;
  end;
  dom Funcs({},f) = dom f by Def8;
  hence thesis by A1,FUNCOP_1:11;
end;
