theorem Th1: :: SETWOP_2:1

for C, D being non empty set
for c1, c2 being Element of C
for F being BinOp of D
for f being Function of C,D st F is commutative & F is associative & c1 <> c2 holds
F $$ ({.c1,c2.},f) = F . ((f . c1),(f . c2))