ELis a family of tractable Description Logics (DLs) that is the basis of the OWL 2 EL profile. Unlike for many expressive DLs, reasoning inELcan be performed by computing a deductively-closed set of logical consequences of some specific form. In some ontology-based applications, e.g., for ontology de- bugging, knowing the logical consequences of the ontology axioms is often not sufficient. The user also needs to know from which axioms and how the consequences were derived. Although it is possible to record all inference steps during the application of rules, this is usually not done in practice to avoid the overheads. In this paper, we present a goal-directed method that can generate inferences for selectedconsequencesinthedeductiveclosurewithoutre-applyingallrulesfrom scratch.Weprovideanempiricalevaluationdemonstratingthatthemethodisfast and economical for large ELontologies. Although the main benefits are demonstrated for EL reasoning, the method can be potentially applied to many other procedures based on deductive closure computation using fixed sets of rules.