theorem Th14:
  (ex y,z st x = [y,z]) implies x <> x`1 & x <> x`2
proof
  given y,z such that
A1: x = [y,z];
  now
    assume y = x;
    then {{y,z},{y}} in {y} by A1,TARSKI:def 1;
    hence contradiction by TARSKI:def 2;
  end;
  hence x <> x`1 by A1;
  now
    assume z = x;
    then {{y,z},{y}} in {y,z} by A1,TARSKI:def 2;
    hence contradiction by TARSKI:def 2;
  end;
  hence thesis by A1;
end;
