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

theorem Th27:
  x <> y implies <*x,y,z*> -| y = <*x*>
proof
  assume x <> y;
  then y..<*x,y,z*> = 1+1 by Th22;
  then
A1: 1 = y..<*x,y,z*>-1;
  rng<*x,y,z*> = { x,y,z } by Lm2;
  then y in rng<*x,y,z*> by ENUMSET1:def 1;
  hence <*x,y,z*> -| y = <*x,y,z*>| Seg 1 by A1,FINSEQ_4:33
    .= <*x*> by Th4;
end;
