Turning a closet into a secure gun cabinet is a good idea, However.....
1. Closet doors usually open out, and the hinges are on the outside.
If the hinges are not secured, the door can still be removed. Go to
hardware store and buy the security hing/screw studs. They replace
the middle screw in each hing, and make it more difficult to pry the
door out after the hing pins have been removed.
2. Replace the door knob with a standard 1" throw deadbolt. That will
make it more difficult for someone to spread the door edge and frame,
and pop the door open. Note: you may have to deepen the strike
hole for the deadbolt to fully extend.
best, RG