theorem Th18:
  X <> {} & Y <> {} implies for x being Element of [:X,Y:] holds x
  <> x`1 & x <> x`2
proof
  assume
A1: X <> {} & Y <> {};
  let x be Element of [:X,Y:];
  x = [x`1,x`2] by A1,Th15;
  hence thesis by Th14;
end;
