To address the hallucination in generative question answering (GQA) where the answer can not be derived from the document, we propose a novel evidence-enhanced triplet generation framework, EATQA, encouraging the model to predict all the combinations of (Question, Evidence, Answer) triplet by flipping the source pair and the target label to understand their logical relationships, i.e., predict Answer(A), Question(Q), and Evidence(E) given a QE, EA, and QA pairs, respectively. Furthermore, we bridge the distribution gap to distill the knowledge from evidence in inference stage. Our framework ensures the model to learn the logical relation between query, evidence and answer, which simultaneously improves the evidence generation and query answering. In this paper, we apply EATQA to LLama and it outperforms other LLMs-based methods and hallucination mitigation approaches on two challenging GQA benchmarks. Further analysis shows that our method not only keeps prior knowledge within LLM, but also mitigates hallucination and generates faithful answers.