The phenomenon of “hyperintensionality” can be linked to Frege’s famous article “Über Sinn und Bedeutung” (1892). Frege here showed the need in semantics to take account not only of reference but also of the way in which referent is given – and this “mode of presentation” he named sense (Sinn). The basic property of sense (which Frege did not, however, define) is that two expressions, though they differ in sense, may pick out (refer to) the same object. For example (Frege offered other examples), the expression “integer larger than 1 and divisible only by itself and the number 1” certainly differs from the expression “integer having exactly two divisors”, but both expressions pick out, by virtue of their (different) senses, one and the same object, that is, the set of prime numbers. It can be shown that no set-object can have this property. In order that the proof of this important property of set-objects be easily comprehensible, the main part of the paper focuses on an account of the basic characteristics of Tichý’s transparent intensional logic (TIL), in which hyperintensionality is defined as a procedural property. There may seem to be a disproportion between the several pages of the text and the brief and straightforward proof. In this brief proof, however, it is assumed that the concept of construction is clear, that the sense of an expression is represented as a construction, and that the reference (if it exists) is that which the sense-construction construes, so that the property of Frege’s sense given by the statement VS can be thus formulated by an assertion concerning not expressions, but primarily the relation between sense and referent, for example thus: Two differing senses can be the mode of presentation of the same object (referent). The preponderance of text providing concise information about the basic concepts of TIL over the proof itself can therefore be easily explained.