The two previous posts are correct, but in case you're wondering here's why :
A phono stage is both an amplifier AND an equalizer. It amplifies, and it also greatly boosts the bass, and cuts the treble (according to the RIAA frequency response curve). When the record is pressed the reverse is done (cut bass, boost treble) to maximize the signal to noise on the vinyl medium.
so if you run through 2 phono stages you'd likely get tons of bass and very very little treble (and perhaps cause damage since phono inputs typically expect smaller voltages than line inputs). In theory it should sound lousy. For fun (?!) you could try connecting a turntable with a high output cartridge directly to a line input. You'd expect to hear very little bass and loads of treble .. the opposite from the above.
CD player outputs (and line inputs) in comparison require no equalization, since CD's don't require that the source material be equalized prior to recording (since large amounts of bass are not going to "throw the laser out of the groove").
Sorry if I've just bored you to death, or told you what you already know ... if you're like me you'll like to know why you should do / not do something, rather than just to do/not do it.
All the best