View source for Derived rule

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''of a derivation in a given calculus''

A [[Derivation rule|derivation rule]] whose conclusion is derivable from its premises in the calculus under consideration. For example, in [[Propositional calculus|propositional calculus]] the derivation rule

$$\frac{A\supset B,B\supset C}{A\supset C}$$

is a derived rule, since in this calculus there is derivability from the premises:

$$A\supset B,B\supset C\vdash A\supset C.$$

Every derived rule is a [[Sound rule|sound rule]], but not every sound rule is a derived rule. For example, the [[Substitution rule|substitution rule]] in propositional calculus is a sound but not a derived rule.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  S.C. Kleene,   "Introduction to metamathematics" , North-Holland  (1951)</TD></TR></table>

[[Category:Logic and foundations]]