If you're starting from outside of Yosemite, that's what you're supposed to do. Your wilderness permit should be valid for the entire trip, but must be issued by the agency managing your starting trailhead location.
http://www.nps.gov/yose/planyourvisit/wildpermits.htmQuote
Permits for and from areas outside Yosemite
If you are starting a hike from a trailhead located outside of Yosemite National Park, obtain your permit from the trailhead's managing agency, even if camping in Yosemite. Only one permit is required. Even if you plan to spend every night of a Wilderness trip inside Yosemite but your entry trailhead is outside Yosemite, you do not get the permit from Yosemite. If you are starting at a trailhead in Yosemite and wish to camp outside of Yosemite during your Wilderness trip, you will only need to get a single wilderness permit from Yosemite.
