 For a list of the axioms and rules of intuitionistic first order logic see Gödel 1958, reprinted with detailed introductory note by A.S. Troelstra in Gödel 1990. See also Troelstra 1973, and Troelstra’s “Aspects of constructive mathematics” in Barwise 1977. For a detailed proof of the above theorem the reader is referred also to the latter.