reserve x,y,z for set;
reserve f,f1,f2,f3 for FinSequence,
  p,p1,p2,p3 for set,
  i,k for Nat;
reserve D for non empty set,
  p,p1,p2,p3 for Element of D,
  f,f1,f2 for FinSequence of D;

theorem Th53:
  p1 <> p2 implies <*p1,p2*>:-p2 = <*p2*>
proof
  assume
A1: p1 <> p2;
  p2 in { p1,p2 } by TARSKI:def 2;
  then p2 in rng<*p1,p2*> by Lm1;
  hence <*p1,p2*>:-p2 = <*p2*>^(<*p1,p2*> |-- p2) by Th41
    .= <*p2*>^{} by A1,Th33
    .= <*p2*> by FINSEQ_1:34;
end;
