= Disjunction introduction rule
= Disjunction introduction
{synonym}
The <disjunction introduction rule> in <natural deduction> permits either inference
$$
\frac{A}{A\lor B},\qquad \frac{B}{A\lor B}.
$$
Here $A$ and $B$ are <propositions>, and $\lor$ denotes <logical disjunction>. Establishing either disjunct is sufficient to establish the compound proposition.
The <truth table> explains soundness in classical <propositional logic>: every assignment making the premise true makes the conclusion true. For example, a proof of $x=0$ also proves $x=0\lor x=1$, without requiring a proof of $x=1$.
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