reserve E,X,Y,x for set;
reserve A,B,C for Subset of E;

theorem
  A \ B = A /\ B`
proof
  A in bool E by Def1;
  then
A1: A c= E by ZFMISC_1:def 1;
  thus A /\ B` = (A /\ E) \ B by XBOOLE_1:49
    .= A \ B by A1,XBOOLE_1:28;
end;
