 If \(\delta\) is replaced by the first part of a complex expression, e.g., \(Cq\) or \(CCq0\), then simply adjoining a variable such as \(p\) to give \(Cqp\), \(CCq0p\), is straightforward. But if the “gap” where the variable is to go is not at the end, such as \(Cpq\), or if the variable is to be inserted more than once, as \(CCp0p\), this simple replacement procedure will not work. Leśniewski got around the problem by introducing auxiliary definitions which maneuvered the required variable slot into the right position with only one occurrence. But Łukasiewicz found this procedure unintuitive and wasteful. His preference—which in fact echoes the practice of Frege—was to allow any context in which a single propositional variable is free to serve as a substituend for a functor like \(\delta\), and mark the places into which the argument of \(\delta\) was to be slotted with an apostrophe, so in our examples \(C \apos q\), \(CC\apos 0 \apos\). This more liberal “substitution with apostrophe” allows definitions to be given a satisfyingly simple implicational form. For example, in propositional calculus based on implication and the propositional constant 0, negation can be defined simply by \(C\delta Np\delta Cp0\). The use of variable functors with liberal substitution enables a number of principles of propositional logic to be given startlingly compressed and elegant formulations, for example the principle of bivalence in the form