That there is no mention of truth does not mean that truth isn't there anyway. What does it mean to say that the conclusion is derived from the premises?

Why not? I can derived the statement 1110111 given the initial condition of 0, and the rule x-> 1x1. One can get 1110111 by apply the rule to 0 three times. The is nothing wrong with seeing formal structure of logic as rules and operations.

The question was what does it mean to derive this from that. Not to give me further examples of derivation. Please answer the question. Don't give me another example of derivation.

I think your question is crazy. It is like asking people what it means to walk. I bet you already know how to walk, so why do you need to know what it means to walk? "Derivation" is a primitive. To ask such a basic notion is like asking what is the deal with walking. You know how to do it. You don` t need to know why.

Whether or not I know what it means to walk is one question. Whether I need to know what it means to walk is a different question. You are fairly good at diversion, but not good at answering. Try answering the question, please without diverting it to something else. "Derivation" is not a primitive, since I can define it.

Next.