Existing large language model (LLM)-based table question answering (TableQA) methods primarily involve decomposition reasoning and answer verification processes. However, decomposing questions solely at the semantic level, without considering the factual evidence in tables, fails to significantly reduce the difficulty for LLMs in understanding the key information in questions. Furthermore, reasoning and verification without supporting factual evidence are often arbitrary and unreliable. In light of these issues, this paper proposes a Syllogism-Inspired Reasoning and Verification method (SIRV), which performs reliable decomposition reasoning and answer verification based on the evidential concept of syllogism. Specifically, SIRV extracts question-relevant factual evidence from the table to construct the premises. Based on the constructed premises, SIRV plans reasoning paths and generates sub-questions that explicitly indicate relevant factual evidence, performing evidence-centered reasoning. Additionally, SIRV examines the consistency between the premises and the table to focus on factual evidence, thereby reliably identifying and correcting errors in the reasoning process. Compared to state-of-the-art methods, SIRV achieves performance improvements of up to 5.24% in single-mode and 2.89% in joint reasoning, while also demonstrating excellent generalization ability and efficiency.