Propositional Axioms

Propositional Axioms

$\phi$ a formula of $\mathcal{L}$ obtained from a propositional tautology $\psi$ by substituting simultaneously and uniformly, formulas of $\mathcal{L}$ for the propositional symbols in $\psi$. Then $\phi$ is a propositional axiom for first-order-logic.

Propositional Tautology

A propositional tautology is a propositional formula $\phi$ which takes the value $T$ for every valuation $v$.

Propositional tautology $P\vee \neg P$ $P\to (Q\to P)$