theorem Th7:
  -- (F \ G) = (--F) \ (--G)
proof
  let i;
  hereby
    assume i in --(F\G);
    then
A1: -i in F \ G by Th2;
    then not -i in G by XBOOLE_0:def 5;
    then
A2: not i in --G by Th2;
    i in --F by A1,Th2;
    hence i in (--F) \ --G by A2,XBOOLE_0:def 5;
  end;
  assume
A3: i in (--F) \ --G;
  then not i in --G by XBOOLE_0:def 5;
  then
A4: not -i in G by Th2;
  -i in F by A3,Th2;
  then -i in F \ G by A4,XBOOLE_0:def 5;
  hence thesis by Th2;
end;
