WFFs of PropLog of Length 1

Theorem
The only WFFs of propositional calculus of length $$1$$ are:
 * The letters of $$\mathcal L_0$$;
 * The tautology symbol $$\top$$;
 * The contradiction symbol $$\bot$$.

Proof
We refer to the rules of formation.

From $$\mathbf W: TF$$, $$\top$$ and $$\bot$$ (both of length 1) are WFFs.

From $$\mathbf W: \mathcal P_0$$, every element of $$\mathcal P_0$$ (all of length 1) are WFFs.

Every other rule of formation of propositional calculus consists of an existing WFF in addition to at least one other primitive symbol.

Hence the result.