It is common opinion that relation between the Aristotelian logic (categorical syllogism) and logic of the Stoic is either complemental or rival. In his analysis, the author criticize claim according to which the Stoic examples of conclusions do not contained universal statements. He is showing that they expressed universal statements standard across implication and by anaphoric connection of pronouns. For this reason it is necessary to revise interpretation of basic, so called unprovable inferring rules of the Stoic. These rules are for predicate logic (with relations) and their interpretation, as propositional rules, is just special case. On the base of revised rules the author proved through Stoic logical system all valid modes of the first syllogistic figure of Aristotelian categorical syllogism. He also concludes that Aristotelian logic was just fragment of evidently more strong Stoic logic.