theorem Th16: :: SETWOP_2:16

for C, D, E being non empty set
for B being Element of Fin C
for F being BinOp of D
for f being Function of C,D
for H being BinOp of E
for h being Function of D,E st F is commutative & F is associative & F is having_a_unity & H is commutative & H is associative & H is having_a_unity & h . (the_unity_wrt F) = the_unity_wrt H & ( for d1, d2 being Element of D holds h . (F . (d1,d2)) = H . ((h . d1),(h . d2)) ) holds
h . (F $$ (B,f)) = H $$ (B,(h * f))