In everyday life, people untrained in formal logic draw simple deductive inferences from linguistic material (i.e., elementary propositional deductions). Presently, we have limited information on the brain areas implicated when such conclusions are drawn. We used event-related fMRI to identify these brain areas. A set of multiple and independent criteria was derived from the two main theories in the field of reasoning to maximize the reliability of detection of areas in which activity is specifically associated with deductive inferences. Two left lateralized clusters of areas, one in frontal cortex (Brodmann Area 44 and 6) and one in parietal lobe (BA 40), satisfied all criteria; activation was present at the moment of inference, it was shared by both conditional ("if-based") and disjunctive ("or-based") inferences but was greater for disjunctive clauses. Identification of the reasoning network was corroborated by the observation that activity in these areas was greater the longer the reasoning time. Taken together with results from preceding studies, our findings suggest possible theoretically relevant dissociations between elementary propositional deductions and other types of deductive reasoning.