Deduction theorem

The Deduction Theorem is a fundamental principle in propositional logic and mathematical logic. It establishes a relationship between syntactic proofs and semantic entailment. The theorem can be stated as follows: If a formula \( B \) can be derived from a set of premises \( \Gamma \) along with an additional assumption \( A \), then it is possible to infer that the implication \( A \rightarrow B \) can be derived from the premises \( \Gamma \) alone.