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I'm struggling to learn logic and I'm stuck on what I'm sure is an easy answer. Here's the question:

*whenever p is true, q is true. Whenever q is true, r is true. Prove that, whenever p is true, r is true.*

Here's part of the answer:

*p=>q Premise*

q=>r Premise

(q=>r) => (p => (q=>r)) Implication Introduction

q=>r Premise

(q=>r) => (p => (q=>r)) Implication Introduction

...etc

I can follow the proof just fine from this point. However, why can we assume p is true? The

*Implication Introduction*step is allowing us to assume p is true..even when it's not a premise (or at least they don't state it as a premise explicitly).

Anyway, like I said, I'm sure this is easy, I'm just not wrapping my head around it.

Any help would be appreciated. Thanks guys!