将新闻事实核查文章中的证据提炼为可复用的独立语句，提升自动验证效果。

Fact-checking articles encode rich supporting evidence and reasoning, yet this evidence remains largely inaccessible to automated verification systems due to unstructured presentation. We introduce PrimeFacts, a methodology and resource for extracting fine-grained evidence from full fact-checking articles. We compile 13,106 PolitiFact articles with claims, verdicts, and all referenced sources, and we identify 49,718 in-article hyperlinks as natural anchors to pinpoint key evidence. Our framework leverages large language models (LLMs) to rewrite these anchor sentences into stand-alone, context-independent premises and investigates the extraction of additional implicit evidence. In evaluations on cross-article evidence retrieval and claim verification, the extracted premises substantially improve performance. Decontextualized evidence yields higher retrievability, achieving up to a 30 percent relative gain in Mean Reciprocal Rank over verbatim sentences, and using the evidence for verdict prediction raises Macro-F1 by 10-20 points over the baseline. These gains are consistent across different verdict granularities (2-class vs. 5-class) and model architectures. A qualitative analysis indicates that the decontextualized premises remain faithful to the original sources. Our work highlights the promise of reusing fact-checkers' evidence for automation and provides a large-scale resource of structured evidence from real-world fact-checks.