the use of the word necessary in (7) often causes confusion. Notice that to say that ψ is a necessary condition for ϕ does not mean that ψ on its own is enough to guarantee ϕ. Rather what it says is that ψ will have to hold before there can even be any question of ϕ holding. For that to be the case, ϕ must imply ψ. (This is another of those occasions where my strong advice would be to re-read this paragraph several times until you are sure you get the point—then read it at least one more time!)
