“Human” in Mises’ works is basically defined as an actor. So the above statement is tantamount to “Acting beings are acting beings.”
I think people who virtually only read Rothbard, Hoppe, and others, and not Mises himself, would be surprised to know that Mises did not use the term “axiom” once in Human Action or Theory and History. And I don’t think he ever used the term “action axiom”.
Praxeology is not a grammatical exercise. It is not an unbundling of the meaning of a proposition. It is an unbundling of the meaning of a conception already present in all our minds.
Praxeology is the result of reflecting on the essence of the conception we think of when we hear the single word “action”, not the result of reflecting on the meaning of the proposition “action is purposeful behavior”.
When Mises brings in the term “purposeful behavior”, he does so as a clarifying substitute for “action”, just in case readers are thinking of another meaning of the word “action”, not as the second half of proposition from which to derive theorems.
Just as much as we can say that “praxeology is the result of reflecting on the essence of action”, and then just stop there, we can also say that “praxeology is the result of reflecting on the essence of purposeful behavior” and just stop there. We’d be saying the same thing.
For more on Mises’ ideas about apriorism and praxeology, please read the paper in my sig.