 ##  [Completeness Theorem](/completeness-theorem) 

  ##  [Completeness Theorem](https://mathlogic.quantumdictionary.io/completeness-theorem-0) 

  
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- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A metatheorem, classically for first-order logic, stating that if a formula is semantically entailed by a set of sentences then it is syntactically provable from those sentences; semantic consequence implies syntactic derivability (Σ ⊨ φ implies Σ ⊢ φ).