Personally, I've read lots of logic texts, so the above *'symbol salad'* seems completely normal to me.

In English, your *'symbol salad'* just says, "there exists some common \\(b\\) such that the feasibility relation \\(\phi\\) between \\(a\\) and \\(b\\) holds, and there exists some common \\(c\\) such that the feasibility relations \\(\psi\\) between \\(b\\) and \\(c\\) holds, and the feasibility relation \\(\nu\\) between \\(c\\) and \\(d\\) holds, if, and only if, there exists some common \\(c\\) such that there exists some common \\(b\\) such that the feasibility relation \\(\phi\\) between \\(a\\) and \\(b\\) holds, the feasibility relations \\(\psi\\) between \\(b\\) and \\(c\\) holds, and the feasibility relation \\(\nu\\) between \\(c\\) and \\(d\\) holds."