Let phi be the normal density function (i.e. the Gaussian), and let F be the forward price, K the strike, V the volatility and T time to expiry. Define d1 and d2 as follows

d1 = (LN(F / K) + V ^ 2 * T / 2) / (V * SQRT(T))

d2 = (LN(F / K) - V ^ 2 * T / 2) / (V * SQRT(T))

The odd result is that

F phi(d1) = K phi(d2)

It's easily proved by substituting the standard exponential formula for the Gaussian. Then there is a load of cancellation and you find the ratio of phi(d1) to phi(d2) = exp(ln(K/F)) = K/F

Is there any textbook reference for this, or has it been noted by others?