reserve a,b,d,n,k,i,j,x,s for Nat;

theorem Th23:
  for n be non zero Nat holds 0 in rng pfexp n
proof
  let n be non zero Nat;
  not SetPrimes c= support pfexp n;
  then consider p be object such that
A1: p in SetPrimes & not p in support pfexp n by TARSKI:def 3;
  reconsider p as Prime by A1,NEWTON:def 6;
  dom pfexp n = SetPrimes & (pfexp n).p = 0
    by A1,PRE_POLY:def 7,PARTFUN1:def 2;
  hence thesis by A1,FUNCT_1:def 3;
end;
