set UFX = union FX;
set UCFX = union (clf FX);
for x being Point of T st x in union (clf FX) holds
x in union FX

let x be Point of T; :: thesis:
assume x in union (clf FX) ; :: thesis:
then consider X being set such that
A3: x in X and
A4: X in clf FX by TARSKI:def 4;
reconsider X = X as Subset of T by A4;
consider W being Subset of T such that
A5: X = Cl W and
A6: W in FX by A4, Def2;
reconsider W = W as Subset of T ;
W is closed by A2, A6, TOPS_2:def 2;
then x in W by A3, A5, PRE_TOPC:22;
hence x in union FX by A6, TARSKI:def 4; :: thesis:

end;

end;