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

theorem Th34:
  x <> z & y <> z implies <*x,y,z*> |-- z = {}
proof
  assume that
A1: x <> z and
A2: y <> z;
A3: len<*x,y,z*> = 3 by FINSEQ_1:45;
  z in { x,y,z } by ENUMSET1:def 1;
  then
A4: z in rng<*x,y,z*> by Lm2;
  z..<*x,y,z*> = 3 by A1,A2,Th23;
  hence thesis by A4,A3,FINSEQ_4:49;
end;
