Rule of Sequent Introduction

Theorem
Let the statements $P_1, P_2, \ldots, P_n$ be conclusions in a proof, on various assumptions.

Let $P_1, P_2, \ldots, P_n \vdash Q$ be a sequent for which we already have a proof.

Then we may infer, at any stage of a proof (citing SI), the conclusion $Q$ of the sequent already proved.

This conclusion depends upon the pool of assumptions upon which $P_1, P_2, \ldots, P_n$ rest.

This is called the rule of sequent introduction.

Proof
By hypothesis we have a proof of:
 * $P_1, P_2, \ldots, P_n \vdash Q$

Therefore we can include this proof in our current proof and arrive at $Q$ with the pool of assumptions upon which $P_1, P_2, \ldots, P_n$ rest.

Also known as
This rule is also known as the rule of replacement.

Also see

 * Rule of Theorem Introduction, which is a direct corollary of this.