
theorem Th6:
  for p being Prime,
      a being Integer holds a gcd p <> 1 iff p divides a
proof
let p be Prime,
    a be Integer;
  hereby assume a gcd p <> 1;
   then a gcd p = p by INT_2:21,INT_2:def 4;
   hence p divides a by INT_2:21;
  end;
  assume A1: p divides a;
  p divides (a gcd p) by A1,INT_2:22;
  hence a gcd p <> 1 by INT_2:27,INT_2:def 4;
end;
