In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly axiomatize that hypothesis, i.e. to prove an implication A → B {\displaystyle A\to B} , it is sufficient to assume A {\displaystyle A} as a hypothesis and then proceed to derive B {\displaystyle B} .
In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly axiomatize that hypothesis, i.e. to prove an implication A → B {\displaystyle A\to B} , it is sufficient to assume A {\displaystyle A} as a hypothesis and then proceed to derive B {\displaystyle B} .
Source: Wikipedia "Deduction theorem" · CC BY-SA 4.0
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