The wing (not the engine) lifts the aircraft by creating a lift vector opposite to weight (vertically down). With any angle of bank, the actual lift vector has to be greater than weight, since there is a horizontal component to add. Therefore the lift force at the same airspeed is greater, so alpha must increase. If you are already at max alpha, then you stall, alternatively you increase airspeed to increase lift at the same alpha.
QED.