Document-level Relation Extraction (DocRE) aims to identify and extract relations between entities from entire documents. Unlike sentence-level relation extraction, document-level relation extraction requires considering cross-sentence contextual information to capture complex relations expressed across multiple sentences or paragraphs. Previous research has shown that the application of Logical Rules (LR) can improve the efficiency of relation extraction. However, identifying and extracting these logical rules require significant memory consumption, and the obtained logical rules lack specificity. To address this issue, we propose a novel approach in this paper (ELRSD (The implementation code for ELRSD can be obtained from the GitHub link: https://github.com/maoxuxu/elrsd .)), Based on the Self-Distillation (SD) training process, utilize Multi-head Graph Convolution Networks and Transformer synergistic learning to improve the extraction of logical rules, thereby enhancing the extraction of entity relations. We conduct comprehensive experiments on three popular benchmark datasets. The results obtained under the same experimental settings indicate that our method achieved state-of-the-art performance.