That is true for any single mirror or lens system. Take the equation magnification = -(distance of image/distance of object). By this equation, any time the object and image distance have the same sign, the magnification will be negative and the image will be inverted. By convention, any time the object and image distance have the same sign, the image is real (this can be confusing because when an object and image are on the same side of a lens, they have opposite signs). Conversely, when the image and object have opposite signs, by this equation the image is not inverted, and by convention, it is virtual.
However, in multi-lens/mirror systems this is not necessarily true. You could end up with an inverted virtual image or an upright real image.
