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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: 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.

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.

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?

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: 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.

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. 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: 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.

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?