Is the contribution limit on 403(b) plans reduced if you also contribute to an IRA?
It's the other way around. Your ability to contribute to a deductible IRA is reduced or eliminated depending on your gross income if you participate in the 403(b). And it doesn't matter how much you contribute to the work plan -- if you are covered by a work plan in any amount, you have to check your income to see if you can make deductible IRA contributions.