Propositional Formula

A set $\mathcal{F}$ of items in PV with propositional closure properties

Definition

Let $\mathcal{F}$ be the smallest set s.t

Basis

For every $x\in PV,x\in \mathcal{F}$

Ind Step

If $p_1,p_2\in \mathcal{F}$ Then, $\neg p_1,(p_1\wedge p_2),(p_1\vee p_2),(p_1⟹p_2),(p_1⟺p_2)\in \mathcal{F}$