Language of Predicate Logic has Unique Parsability

Theorem
Each WFF of predicate logic which starts with a left bracket or a negation sign has exactly one main connective.

Proof
We have the following cases:
 * 1) $\mathbf A = \neg \mathbf B$, where $\mathbf B$ is a WFF of length $k$.
 * 2) $\mathbf A = \paren {\mathbf B \circ \mathbf C}$ where $\circ$ is one of the binary connectives.
 * 3) $\mathbf A = \map p {t_1, t_2, \ldots, t_n}$, where $t_1, t_2, \ldots, t_n$ are terms, and $p \in \PP_n$.
 * 4) $\mathbf A = \paren {Q x: \mathbf B}$, where $\mathbf B$ is a WFF of length $k - 5$, $Q$ is a quantifier ($\forall$ or $\exists$) and $x$ is a variable.

We deal with these in turn.

Cases 1 and 2 are taken care of by Language of Propositional Logic has Unique Parsability.

Cases 3 and 4 do not start with either a left bracket or a negation sign, so do not have to be investigated.