reserve a,b,c,k,m,n for Nat;
reserve i,j,x,y for Integer;
reserve p,q for Prime;
reserve r,s for Real;

theorem Th20:
  primenumber m = primenumber n implies m = n
  proof
    assume
A1: primenumber m = primenumber n;
    assume m <> n;
    then m < n or m > n by XXREAL_0:1;
    hence thesis by A1,MOEBIUS2:21;
  end;
