When light encounters a mirror, regardless of its color, it undergoes reflection rather than transmission. A mirror is a highly reflective surface that reflects incident light back in a specular manner. Therefore, when blue light reaches a mirror, it will be reflected as blue light.
If you are on the opposite side of a TV looking at it through a mirror, the blue light emitted by the TV will still be reflected by the mirror and reach your eyes. The mirror does not selectively filter out or alter the color of the light it reflects. So, as long as the blue light from the TV reaches the mirror, it will be reflected and remain blue when it reaches your eyes.
It's worth noting that the perceived color of an object is determined by the light that reaches our eyes. If the TV emits only blue light, and the mirror reflects that blue light faithfully, you would see the same blue color when looking at the TV through the mirror. However, if there are other colors present in the TV's emission, those colors would also be reflected by the mirror and contribute to the overall color perception.