BLM rules and regulations for Wilderness Areas are codified under…
§ 6304.23 What special provisions apply to mineral leasing and material sales?
(a) After Congress designates any area of public lands as wilderness, BLM will not issue mineral or geothermal leases, licenses, or permits under the mineral or geothermal leasing laws, or sales contracts or free use permits under the Materials Act (30 U.S.C. 601et seq.)
(b) You may continue to hold and operate mineral or geothermal leases, licenses, contracts, or permits under their original terms and conditions after Congress designates the affected BLM lands as wilderness.