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 $$k-3$$, $$Q$$ 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.