theorem
  Ex(x1,y1,z1,p1) = Ex(x2,y2,z2,p2) implies x1 = x2 & y1 = y2 & z1 = z2
  & p1 = p2
proof
  assume
A1: Ex(x1,y1,z1,p1) = Ex(x2,y2,z2,p2);
  then Ex(y1,z1,p1) = Ex(y2,z2,p2) by ZF_LANG:34;
  hence thesis by A1,Th17,ZF_LANG:34;
end;
