Large Language Models (LLMs) demonstrate significant potential in sequential recommendation, and leveraging their Chain-of-Thought (CoT) reasoning capabilities can further unlock profound user preference understanding. However, deploying explicit CoT reasoning in real-world systems faces prohibitive challenges: (i) the conflict between the large model scale required for high-fidelity reasoning and the resource constraints of online services, and (ii) the excessive latency introduced by auto-regressive rationale generation. To address these issues, we propose I Reasoning via Multi-Teacher Distillation (IRMD), a novel framework that 'compiles' the reasoning abilities of large teacher LLMs into a lightweight student Small Language Model (SLM). IRMD first employs a Multi-Teacher CoT Synthesis with Dual-Constraint Rejection Sampling module to generate a high-quality, diverse set of reasoning paths. Subsequently, our Annealing-Scheduled Reasoning Distillation strategy progressively trains the student to internalize this logic, transitioning from mimicking explicit CoT to performing purely implicit reasoning. Extensive experiments on multiple benchmark datasets demonstrate that IRMD significantly outperforms state-of-the-art baselines in both recommendation accuracy and inference efficiency. Our code is accessible at https://github.com/Cxx-0/IRMD.