theorem Th24: :: EUCLIDLP:24

for a1, a2, a3, b1, b2, b3 being Real
for n being Nat
for x1, x2, x3 being Element of REAL n holds (((a1 * x1) + (a2 * x2)) + (a3 * x3)) + (((b1 * x1) + (b2 * x2)) + (b3 * x3)) = (((a1 + b1) * x1) + ((a2 + b2) * x2)) + ((a3 + b3) * x3)