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Visual entailment is a recently proposed multimodal reasoning task where the goal is to predict the logical relationship of a piece of text to an image. In this paper, we propose an extension of this task, where the goal is to predict the logical relationship of fine-grained knowledge elements within a piece of text to an image. Unlike prior work, our method is inherently explainable and makes logical predictions at different levels of granularity. Because we lack fine-grained labels to train our method, we propose a novel multi-instance learning approach which learns a fine-grained labeling using only sample-level supervision. We also impose novel semantic structural constraints which ensure that fine-grained predictions are internally semantically consistent. We evaluate our method on a new dataset of manually annotated knowledge elements and show that our method achieves 68.18\% accuracy at this challenging task while significantly outperforming several strong baselines. Finally, we present extensive qualitative results illustrating our method's predictions and the visual evidence our method relied on. Our code and annotated dataset can be found here: https://github.com/SkrighYZ/FGVE.