 reserve x,y,X1,X2,X3,X4,X5,X6,Y,Y1,Y2,Y3,Y4,Y5,Z,Z1,Z2,Z3,Z4,Z5 for set;
 reserve X for non empty set;

theorem Th1:
  ex Y st Y in X & Y misses X
proof
  consider x being object such that
A1:  x in X by XBOOLE_0:def 1;
  consider Y such that
A2: Y in X and
A3: not ex x be object st x in X & x in Y by A1,TARSKI:3;
  take Y;
  not ex x being object st x in X & x in Y by A3;
  hence thesis by A2,XBOOLE_0:3;
end;
