Large language models (LLMs) can generate factually inconsistent claims, motivating accurate and scalable hallucination detectors. Prior work largely enlarges training sets via synthesis or new annotations, introducing increasing cost and potential bias while underusing the consistency implied by semantically equivalent paraphrases. We propose Consistency-Constrained Hallucination Detector (CCHD), which formulates training as a constrained optimization problem. The standard cross-entropy on original document-claim pairs is complemented by (i) paraphrase-consistency constraints bounding divergence across paraphrased views, and (ii) label-preservation constraints tying paraphrases to ground truth. We solve the problem by gradient descent-ascent over model parameters and per-view Lagrange multipliers, adding only a few scalar dual variables and no inference-time overhead. With DeBERTa and Flan-T5 backbones, CCHD consistently outperforms strong baselines (FactCG, MiniCheck, and AlignScore) on standard factuality benchmarks, demonstrating its superiority on hallucination detection.