I was learning about single slit diffraction, and how if you have a slit such that the path difference between the closest and farthest ray is a natural number m * the wavelength, you will have destructive interference because you can pair rays together that interfere destructively (I was watching these two Khan Academy videos: https://www.khanacademy.org/science/physics/light-waves/interference-of-light-waves/v/single-slit-interference and https://www.khanacademy.org/science/physics/light-waves/interference-of-light-waves/v/more-on-single-slit-interference).
However, this leaves me wondering how you derive the equation for double slits using this logic. Every derivation I have found seems to treat the light coming from each slit as a single ray - and thus, if the path difference between the two rays is an natural number m * lambda, you get constructive interference (even the Khan Academy video does it this way: https://www.khanacademy.org/science/physics/light-waves/interference-of-light-waves/v/youngs-double-slit-part-2). But to me, this seems to ignore the destructive interference that occurs from the infinite parallel rays coming from each slit (if you use the same logic that was used for single slits).
Is there some way to use the same logic as in the single slit proof to show that m corresponds to points of constructive interference in the double slit setup, not of destructive interference?