reserve x,A,B,X,X9,Y,Y9,Z,V for set;

theorem
  X \ Y misses Y \ X
proof
  assume X \ Y meets Y \ X;
  then consider x being object such that
A1: x in X \ Y and
A2: x in Y \ X by XBOOLE_0:3;
  x in X by A1,XBOOLE_0:def 5;
  hence thesis by A2,XBOOLE_0:def 5;
end;
