reserve v,x,x1,x2,x3,x4,y,y1,y2,y3,y4,z,z1,z2 for object,
  X,X1,X2,X3,X4,Y,Y1,Y2,Y3,Y4,Y5,
  Z,Z1,Z2,Z3,Z4,Z5 for set;
reserve p for pair object;

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;
