reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r for Real;
reserve p,p1,p2 for Prime;

theorem
  33 = 3*11 & 33 has_exactly_two_different_prime_divisors
  proof
    thus
A1: 33 = 3*11;
    take P3, P11;
    thus P3 <> P11;
    thus P3 divides 33 by A1;
    thus P11 divides 33 by A1;
    let r be Prime such that
A2: r <> P3 & r <> P11;
    assume r divides 33;
    then r divides 3 or r divides 11 by A1,INT_5:7;
    hence thesis by A2,XPRIMES0:1,XPRIMES1:3,11;
  end;
