theorem :: FILTER_2:2

for D being non empty set
for S being non empty Subset of D
for f being BinOp of D
for g being BinOp of S
for d being Element of D
for d9 being Element of S st g = f || S & d9 = d holds
( ( d is_a_left_unity_wrt f implies d9 is_a_left_unity_wrt g ) & ( d is_a_right_unity_wrt f implies d9 is_a_right_unity_wrt g ) & ( d is_a_unity_wrt f implies d9 is_a_unity_wrt g ) )