Abstractive summarization, the task of rewriting and compressing a document into a short summary, has achieved considerable success with neural sequence-to-sequence models. However, these models can still benefit from stronger natural language inference skills, since a correct summary is logically entailed by the input document, i.e., it should not contain any contradictory or unrelated information. We incorporate such knowledge into an abstractive summarization model via multi-task learning, where we share its decoder parameters with those of an entailment generation model. We achieve promising initial improvements based on multiple metrics and datasets (including a test-only setting). The domain mismatch between the entailment (captions) and summarization (news) datasets suggests that the model is learning some domain-agnostic inference skills.