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."