reserve A for set;
reserve X,Y,Z for set,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve u for UnOp of A,
  o,o9 for BinOp of A,
  a,b,c,e,e1,e2 for Element of A;

theorem
  for f being Function of [:X,Y:],Z st x in X & y in Y & Z <> {} holds f
  .(x,y) in Z
proof
  let f be Function of [:X,Y:],Z;
  assume x in X & y in Y;
  then [x,y] in [:X,Y:] by ZFMISC_1:87;
  hence thesis by FUNCT_2:5;
end;
