Set of First Order Predicate Formula

Definition

A Proof by Structural Induction definition

Basis

Any Atomic Formula is in the set

Induction Step

If $F_1,F_2\in S$ and $x$ is a Variable, then $\neg F_1$, $(F_1\wedge F_2)$, $(F_1\vee F_2)$, $(F_1\to F_2)$, $(F_1\leftrightarrow F_2),(\exists x{F}_1,\forall x{F}_1)$ are in the set