
theorem Th24:
  for f being Function, x,y being set holds [x,y] in graph f iff x
  is finite & x in dom f & y in f.x
proof
  let f be Function, x,y be set;
  now
    given y9 being finite set, z being set such that
A1: [x,y] = [y9,z] and
A2: y9 in dom f & z in f.y9;
    x = y9 by A1,XTUPLE_0:1;
    hence x is finite & x in dom f & y in f.x by A1,A2,XTUPLE_0:1;
  end;
  hence thesis by Def16;
end;
