Inference rule

An inference rule is a representation of a valid step in a formal proof, indicating the conditions that must be satisfied before a conclusion can be obtained in the proof.

A rule will be presented in the form: $R:\frac{A_1,A_2,...,A_n}{B}$

$A_1,A_2,...,A_n$ are the premises or conditions of the rule, and $B$ is the conclusion.

Informally, $R:$ “if $A_1,A_2,...,A_n$ are true, then $B$ is also true.”

Alternatively, we use the syntax:

$$\begin{array}{c}{A}_1\\ A_2\\ ⋮\\ A_n\\ B\end{array}$$