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As deep neural networks (DNNs) get adopted in an ever-increasing number of applications, explainability has emerged as a crucial desideratum for these models. In many real-world tasks, one of the principal reasons for requiring explainability is to in turn assess prediction robustness, where predictions (i.e., class labels) that do not conform to their respective explanations (e.g., presence or absence of a concept in the input) are deemed to be unreliable. However, most, if not all, prior methods for checking explanation-conformity (e.g., LIME, TCAV, saliency maps) require significant manual intervention, which hinders their large-scale deployability. In this paper, we propose a robustness-assessment framework, at the core of which is the idea of using machine-checkable concepts. Our framework defines a large number of concepts that the DNN explanations could be based on and performs the explanation-conformity check at test time to assess prediction robustness. Both steps are executed in an automated manner without requiring any human intervention and are easily scaled to datasets with a very large number of classes. Experiments on real-world datasets and human surveys show that our framework is able to enhance prediction robustness significantly: the predictions marked to be robust by our framework have significantly higher accuracy and are more robust to adversarial perturbations.