
theorem PQCoprime:
  for p,q being Prime st p <> q holds p,q are_coprime
  proof
    let p,q be Prime;
    assume
A1: p <> q;
    p gcd q <> p
    proof
      assume p gcd q = p; then
      p divides q by INT_2:def 2; then
      p = q or p = 1 by INT_2:def 4;
      hence thesis by A1,INT_2:def 4;
    end;
    hence thesis by NEWTON03:46;
  end;
