 ##  [Deduction Theorem](/index.php/deduction-theorem) 

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

  
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- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A metatheorem relating syntactic provability to implication: if a formula B is provable from assumption A (possibly together with other assumptions), then the implication A → B is provable in the surrounding formal system, subject to system-specific conditions about discharged assumptions.