theorem
  for f ex g being Function of C,D st for c st c in dom f holds g.c = f /.c
proof
  let f;
  consider g being Function of C,D such that
A1: for x being object st x in dom f holds g.x = (f qua Function).x
    by FUNCT_2:71;
  take g;
  let c;
  assume
A2: c in dom f;
  then g.c = (f qua Function).c by A1;
  hence thesis by A2,PARTFUN1:def 6;
end;
