Bottom-Up Specification of Propositional Logic/Examples/Example 1

Example of Bottom-Up Specification of Propositional Logic
The following is a WFF of propositional logic:
 * $\paren {\paren {p \land q} \implies \paren {\lnot \paren {q \lor r} } }$

Proof
It is assumed that $p$, $q$ and $r$ are WFFs by $\mathbf W: \PP_0$.

By $\mathbf W: \text {OP}$:
 * $\paren {p \land q}$ is a WFF
 * $\paren {q \lor r}$ is a WFF

By $\mathbf W: \neg$:
 * $\paren {\lnot \paren {q \lor r} }$ is a WFF

By $\mathbf W: \text {OP}$:
 * $\paren {\paren {p \land q} \implies \paren {\lnot \paren {q \lor r} } }$ is a WFF