How Safe Is Taking Prozac,Synthroid And Cymbalta All Together?

I have been on Xanax 0.5 mg twice a day and prozac 30 mg once a day for 2 years. I m also on synthroid .25 mg. I went to see a psychiatrist today. He put me on Cymbalta 30mg. Twice a day. Is it safe to take these meds together. I will go back to him in a month to see how I m doing. If I do okay he will then take me off prozac.