
theorem tA:
for R being 0-characteristic domRing,
    a being Element of R
holds -a = a iff a = 0.R
proof
let R be 0-characteristic domRing, a be Element of R;
hereby assume -a = a;
then a + a = 0.R by RLVECT_1:5;
then C: 0.R = (1 '*' a) + a by RING_3:60
           .= (1 '*' a) + (1 '*' a) by RING_3:60
           .= (1+1) '*' a by RING_3:62;
Char R = 0 by RING_3:def 6;
then a is zero by C,char4;
hence a = 0.R;
end;
thus thesis;
end;
