reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;

theorem
  for x,y,z being variable holds
  <*x,y,z*> is quasi-loci iff vars x = {} & x <> y & vars y c= {x} &
  x <> z & y <> z & vars z c= {x,y}
proof
  let x,y,z be variable;
A1: rng <*x,y*> = {x,y} by FINSEQ_2:127;
A2: <*x,y*> is quasi-loci iff vars x = {} & x <> y & vars y c= {x} by Th35;
  z in {x,y} iff z = x or z = y by TARSKI:def 2;
  hence thesis by A1,A2,Th31,Th32;
end;
