# Rule of Theorem Introduction

## Definition

We may introduce, at any stage of a proof (citing TI), a theorem already proved, or a substitution instance of such a theorem, together with a reference to the theorem that is being cited.

## Proof

This theorem is a corollary of the Rule of Sequent Introduction.

$\blacksquare$

## Application

Using this rule, we can use theorems that we have derived in order to shorten proofs which may otherwise be long and unwieldy.

## Technical Note

When invoking Rule of Theorem Introduction in a tableau proof, use the {{TheoremIntro}} template:

{{TheoremIntro|line|statement|theorem}}

where:

line is the number of the line on the tableau proof where the Rule of Theorem Introduction is to be invoked
statement is the statement of logic that is to be displayed in the Formula column, without the $...$ delimiters
theorem is the link to the theorem in question that will be displayed in the Notes column.