Language of Predicate Logic has Unique Parsability

Theorem
Each WFF of predicate calculus 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) $\mathbf A = \left({\mathbf B \circ \mathbf C}\right)$ where $\circ$ is one of the binary connectives.
 * 3) $\mathbf A = p \left({u_1, u_2, \ldots, u_n}\right)$, where $u_1, u_2, \ldots, u_n$ are individual symbols, and $p \in \mathcal P_n$.
 * 4) $\mathbf A = ( Q x: \mathbf B )$, 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 the Unique Readability Theorem of Propositional Calculus.

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