theorem :: RING_3:22

for m, n being Nat
for i, j being Integer st m <> 0 & n <> 0 holds
( denominator ((i / m) + (j / n)) = (m * n) / (((i * n) + (j * m)) gcd (m * n)) & numerator ((i / m) + (j / n)) = ((i * n) + (j * m)) / (((i * n) + (j * m)) gcd (m * n)) )