Alan, if both individual headers are within 3' of same or different bearing, you will be fine, per code. "Single trimmer joists may be used to carry a single header joist that is located within 3 feet (914 mm) of the trimmer joist bearing." Bold/underline is mine.
Code is minimum though there is a safety factor with the span ratings. eg.- 2x6 D.F.@ 16"o.c. w. 8' span = 89# lin.ft. or 711# dist. load Same at 9' span = 68# or 631# Same at 10' span = 56# or 568# total. From a joist/beam chart L360 w. D.f.