
theorem fresh2:
for p being Prime
for R being p-characteristic commutative Ring
for a being Element of R holds -(a|^p) = (-a)|^p
proof
let p be Prime, R be p-characteristic commutative Ring, a be Element of R;
(-a)|^p - -(a|^p) = (-a + a)|^p by fresh
                 .= (0.R)|^p by RLVECT_1:5
                 .= 0.R;
hence thesis by RLVECT_1:21;
end;
