When using Live view, the camera does use a first curtain electronic shutter, since the sensor is already exposed to light when you press the button to take the picture. But then the mechanical shutter is used to end exposure and keep the sensor in the dark during image readout. This has the disadvantage that the sensor has to be cleared before exposure starts, compared to a sensor that's active already when the shutter button is half-pressed and just requires the shutter to open to capture the image.