Need clarification on HA study Guide

Economics Political Theory
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I read HA years ago and now I am going through the study guide as a primer to get back up to speed. In the technical notes murphy writes, “Mises distinguishes between a priori and a poste- riori statements (see “Why It Matters” above). Hans-Hermann Hoppe draws on Kant to apply yet another distinction, that between analytic and synthetic statements. (Analytic can be deter- mined simply by analyzing the components of the proposition—e.g., “A bachelor is an unmarried male”—while synthetic statements add to our knowledge; they refer to the “real world” and are not merely definitional.) Hoppe argues that Mises’s grand achievement was to prove the existence of true, synthetic, a priori propositions— something that Hume and other philosophers considered impossible.”

What proposition, exactly, shows that mises proved it was possible to have a synthetic statement that was both true, and a priori? I feel like I am gonna have a “duh” moment here in a bit but the foot note doesnt appear to reference a particular statement in the guide.

Here is the guide - page 16

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Human action is purposeful behavior.

Action cannot be observed in an empirical sense (only physical body movements to be observed) and the truth of this axiom cannot be undone. It’s truth can only be realized through reflective understanding. As such, it is a synthetic axiom that is a priori true.

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“Human action is purposeful behavior.”

Actually, that’s analytic – the concept of “purposeful behavior” is contained in the concept “human action.”

A synthetic a priori proposition would be: “An increase in the supply of money will cause the purchasing power of money to be lower than it would have been otherwise.”

The concept of “lower purchasing power” is NOT contained in the concept “increase in the supply of money,” but the statement can be found true prior to empirical observation.