 The improvement of Bolzano’s version of this traditional proof consists in Bolzano’s explicitly mentioning premise (2) as indispensable for the deduction (WL I, 145, 151; cf. also WL IV, 282 f.), thus making clear that the proof would not go through if this premise were not accepted. The inference of (4) from (3) and (1) is vindicated by Bolzano’s explication of propositional negation (see section 3.4). Bolzano is not content with having proven (allegedly) that there is at least one true proposition; he wants even to prove by mathematical induction that there are more and even infinitely many true propositions (see section 11.2).