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

theorem Th12:
  A c= B iff B` c= A`
proof
  thus A c= B implies B` c= A` by XBOOLE_1:34;
A1: E \ B` = B`` .= B;
  E \ A` = A`` .= A;
  hence thesis by A1,XBOOLE_1:34;
end;
