Completeness theorem for propositional logic
= Completeness theorem for propositional logic
For a set of formulae $\Gamma$ and a formula $\varphi$,
$$
\Gamma\models\varphi\quad\Longrightarrow\quad\Gamma\vdash\varphi.
$$
Together with the <soundness theorem for propositional logic>, this says that semantic consequence and syntactic provability coincide. Equivalently, every <consistent set of formulae> has a satisfying Boolean valuation.
= Propositional completeness theorem
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