Duality shows that valid logical laws remain valid under structured symbol changes. Substitution rules explain another powerful idea: a law proved for primitive statements may be applied to compound statements. This is why laws of logic can simplify long expressions without building a new truth table at every step. In this lesson, substitution rules for logical equivalence will justify replacing statement forms inside larger compound statements.

Let $P$ be a tautology involving primitive statements $p_1,p_2,\ldots,p_n$. If each $p_i$ is replaced by a statement $s_i$, then the resulting statement is also a tautology.