theorem Th53: :: MONOID_1:53

for D being non empty set
for o being BinOp of D st o is having_a_unity holds
( o .:^2 is having_a_unity & {(the_unity_wrt o)} is_a_unity_wrt o .:^2 & the_unity_wrt (o .:^2) = {(the_unity_wrt o)} )