reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve p for Prime;

theorem Th8:
  m > 1 & n > 1 & m,n are_coprime implies
  ex p,q being Prime st p divides m & not p divides n &
   q divides n & not q divides m & p <> q
  proof
    assume m > 1;
    then
A1: m >= 1+1 by NAT_1:13;
    assume n > 1;
    then
A2: n >= 1+1 by NAT_1:13;
    assume
A3: m,n are_coprime;
    consider p being Element of NAT such that
A4: p is prime and
A5: p divides m by A1,INT_2:31;
    consider q being Element of NAT such that
A6: q is prime and
A7: q divides n by A2,INT_2:31;
    reconsider p as Prime by A4;
    reconsider q as Prime by A6;
    take p,q;
    thus thesis by A3,A5,A7,PYTHTRIP:def 2;
  end;
