We introduce VerifAI, an open-source expert system for biomedical question answering that integrates retrieval-augmented generation (RAG) with a novel post-hoc claim verification mechanism. Unlike standard RAG systems, VerifAI ensures factual consistency by decomposing generated answers into atomic claims and validating them against retrieved evidence using a fine-tuned natural language inference (NLI) engine. The system comprises three modular components: (1) a hybrid Information Retrieval (IR) module optimized for biomedical queries (MAP@10 of 42.7%), (2) a citation-aware Generative Component fine-tuned on a custom dataset to produce referenced answers, and (3) a Verification Component that detects hallucinations with state-of-the-art accuracy, outperforming GPT-4 on the HealthVer benchmark. Evaluations demonstrate that VerifAI significantly reduces hallucinated citations compared to zero-shot baselines and provides a transparent, verifiable lineage for every claim. The full pipeline, including code, models, and datasets, is open-sourced to facilitate reliable AI deployment in high-stakes domains.