What begins with two broad statements and arrives at a narrower proposition based on those statements?

This sounds like a syllogism, a type of logical argument that consists of three parts:

* Major premise: A general statement that applies to a large category.

* Minor premise: A specific statement that relates to the category mentioned in the major premise.

* Conclusion: A statement derived from the major and minor premises.

Here's an example:

Major premise: All humans are mortal.

Minor premise: Socrates is a human.

Conclusion: Therefore, Socrates is mortal.

The major premise sets a general rule, the minor premise identifies a specific case that falls under the rule, and the conclusion draws a logical connection between the two.