Consistency is one of the attributes in measuring the quality of UML model. It is the situation where two or more overlapping elements of different diagrams that describe behavior of system are jointly satisfiable. Although there are increasing researches on consistency management, there is still lack of researches of consistency driven by use case. Therefore, this paper proposes three consistency rules between use case and activity diagram. The elements of each diagrams and their consistency are described using logical approach. Based on an example of UML model consists of both diagrams, we show how the diagrams fulfilled our proposed consistency rules. Finally, the elements involved in the consistency rules are detected and formally reasoned.