We study the problem of learning neural text classifiers without using any labeled data, but only easy-to-provide rules as multiple weak supervision sources. This problem is challenging because rule-induced weak labels are often noisy and incomplete. To address these two challenges, we design a label denoiser, which estimates the source reliability using a conditional soft attention mechanism and then reduces label noise by aggregating rule-annotated weak labels. The denoised pseudo labels then supervise a neural classifier to predicts soft labels for unmatched samples, which address the rule coverage issue. We evaluate our model on five benchmarks for sentiment, topic, and relation classifications. The results show that our model outperforms state-of-the-art weakly-supervised and semi-supervised methods consistently, and achieves comparable performance with fully-supervised methods even without any labeled data. Our code can be found at https://github.com/weakrules/Denoise-multi-weak-sources.