a metatheorem is a statement about a formal system proven in a metalanguage. Unlike theorems proved within a given formal system, a metatheorem is proved...

In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly...

φ0. We also use repeatedly the method of the hypothetical syllogism metatheorem as a shorthand for several proof steps. (1) φ 0 {\displaystyle \varphi...

(\neg p\to p)\to p} We also use the method of the hypothetical syllogism metatheorem as a shorthand for several proof steps. p → ( ¬ p → q ) {\displaystyle...

Statements made in the metatheory about the theory are called metatheorems. A metatheorem is a true statement about a formal system expressed in a metalanguage...

problems influenced mathematics for the rest of the 20th century. A metatheorem is defined as: "a statement about theorems. It usually gives a criterion...

conclusion. In most logics, weakening is either an inference rule or a metatheorem if the logic doesn't have an explicit rule. Notable exceptions are: Relevance...

In classical logic, a hypothetical syllogism is a valid argument form, a deductive syllogism with a conditional statement for one or both of its premises...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories....

Hypothetical syllogism. We also use the method of the hypothetical syllogism metatheorem as a shorthand for several proof steps. The proof is as follows: q →...