This work reports on developing a deep learning-based contact estimator for legged robots that bypasses the need for physical contact sensors and takes multi-modal proprioceptive sensory data from joint encoders, kinematics, and an inertial measurement unit as input. Unlike vision-based state estimators, proprioceptive state estimators are agnostic to perceptually degraded situations such as dark or foggy scenes. For legged robots, reliable kinematics and contact data are necessary to develop a proprioceptive state estimator. While some robots are equipped with dedicated contact sensors or springs to detect contact, some robots do not have dedicated contact sensors, and the addition of such sensors is non-trivial without redesigning the hardware. The trained deep network can accurately estimate contacts on different terrains and robot gaits and is deployed along a contact-aided invariant extended Kalman filter to generate odometry trajectories. The filter performs comparably to a state-of-the-art visual SLAM system.