Deduction theorem
In mathematical logic, the deduction theorem is a metatheorem of first-order logic. It is a formalization of the common proof technique in which an implication A → B is proved by assuming A and then deriving B from this assumption conjoined with known results. The deduction theorem explains why proofs of conditional sentences in mathematics are logically correct. Though it has seemed "obvious" to mathematicians literally for centuries that proving B from A conjoined with a set of theorems is sufficient to proving the implication A → B based on those theorems alone, it was left to Herbrand and Tarski to show (independently) this was logically correct in the general case.
primaryTopic
Deduction theorem
In mathematical logic, the deduction theorem is a metatheorem of first-order logic. It is a formalization of the common proof technique in which an implication A → B is proved by assuming A and then deriving B from this assumption conjoined with known results. The deduction theorem explains why proofs of conditional sentences in mathematics are logically correct. Though it has seemed "obvious" to mathematicians literally for centuries that proving B from A conjoined with a set of theorems is sufficient to proving the implication A → B based on those theorems alone, it was left to Herbrand and Tarski to show (independently) this was logically correct in the general case.
has abstract
El teorema de la deducción es ...... s de Jacques Herbrand en 1930.
@es
In mathematical logic, the ded ...... an introduction rule for "→".
@en
Na lógica matemática, o teorem ...... egra de introdução para a "→".
@pt
Nella logica matematica, il te ...... n teorema della stessa teoria.
@it
Twierdzenie o dedukcji – jeżel ...... ych zbioru formuł zdaniowych .
@pl
Unter dem Begriff Deduktionsth ...... ialen Implikation hergestellt.
@de
在数理逻辑中，演绎定理声称如果公式 F 演绎自 E，则蕴涵 ...... 中证明任何东西都是非常困难的。如果你使用了它通常就很容易了。
@zh
演繹定理（英: Deduction theorem）とは、数 ...... 難となる。逆に演繹メタ定理を使えば、証明は非常に簡単になる。
@ja
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Wikipage revision ID
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comment
El teorema de la deducción es ...... bolos: implica implica implica
@es
In mathematical logic, the ded ...... y correct in the general case.
@en
Na lógica matemática, o teorem ...... impando" as práticas matemátic
@pt
Nella logica matematica, il te ...... nferisce , e così via fino a .
@it
Twierdzenie o dedukcji – jeżel ...... ych zbioru formuł zdaniowych .
@pl
Unter dem Begriff Deduktionsth ...... ialen Implikation hergestellt.
@de
在数理逻辑中，演绎定理声称如果公式 F 演绎自 E，则蕴涵 ...... 中证明任何东西都是非常困难的。如果你使用了它通常就很容易了。
@zh
演繹定理（英: Deduction theorem）とは、数 ...... 難となる。逆に演繹メタ定理を使えば、証明は非常に簡単になる。
@ja
label
Deduction theorem
@en
Deduktionstheorem
@de
Teorema da dedução
@pt
Teorema de la deducción
@es
Teorema di deduzione
@it
Twierdzenie o dedukcji
@pl
演繹定理
@ja
演绎定理
@zh