Real-Closed Fields and Intermediate Value Theorem

Question

Artin and Schreier (1926) showed that a real-closed ordered field satisfies the intermediate value theorem for polynomials of a single variable. By the early 1980s authors such as Max Dickmann and Gregory Cherlin, working on the theory of real-closed rings, routinely appealed without proof or reference to the fact that:

For an ordered field $K$, $K$ is real-closed iff $K$ satisfies the intermediate value theorem for polynomials (of a single variable) over $K$.

Since that time numerous proofs of the equivalence have appeared without reference to earlier proofs and some authors, such as van den Dries in his book on o-minimality, simply define a real-closed ordered field as one that satisfies the intermediate value theorem for polynomials (of a single variable). Was the equivalence simply a "folk theorem" by the 1980s or are there earlier published proofs? If the latter, where might one find the earliest such published proof?

Edit 1: I have found a proof of the equivalence in P. Cohn's, Algebra, Volume II, Section 7.4, 1977. I'd still be interested in learning if there are earlier proofs.

Edit 2: As it turns out, already in Modern Algebra by Seth Warner, 1965, pp. 492-494, a real-closed ordered field is essentially defined as an ordered field satisfying the intermediate value theorem for polynomials (in one variable) and the equivalence between that characterization and the more familiar ones is established. I'm beginning to suspect that the equivalence was recognized quite early on for the reason expressed by Emil.

Answer 1

After a bit of searching, it seems reasonable to believe that the explicit recognition of the equivalence goes back to Tarski's great work: The Completeness of Elementary Algebra and Geometry, in The Collected Papers of Alfred Tarski, Vol. IV, Givant, S. R., and McKenzie, R. N., eds. Birkhäuser (1986). (See page 312). The bulk of the paper was written in 1930, three years after Artin and Schreier published their paper, but it wasn't completed and submitted for publication until 1939. Due to the war it didn't go into print until 1967 and the following revised version (that emphasized a decision procedure rather than completeness) was subsequently published: A Decision Method for Elementary Algebra and Geometry 1948/1951. In the latter paper the intermediate value theorem is replaced by a related assertion (See Note 9).

It is interesting to note that in those texts that explicitly say they are closely following the treatment of Artin and Schreier, including van der Waerden's Modern Algebra and Nathan Jacobson's Lectures in Abstract Algebra, there is no hint of the equivalence. The earliest explicit statement of the equivalence I have found in the more recent literature is in the classic text of Seth Warner (1965) mentioned in the second edit of my question. It is also implicit in Nathan Jacobson's Basic Algebra, Vol. 1, 1974 and explicit in P. Cohn's, Algebra, Volume II, Section 7.4, 1977.

Thus, in answer to the question I originally raised, the result appears to have become standard by the 1980s when model theorists and others freely appealed to it.