let V be non empty right_complementable add-associative right_zeroed addLoopStr ; :: thesis: for v being Element of V holds
( v + (- v) = 0. V & (- v) + v = 0. V )
let v be Element of V; :: thesis: ( v + (- v) = 0. V & (- v) + v = 0. V )
thus v + (- v) = 0. V by Def10; :: thesis: (- v) + v = 0. V
hence (- v) + v = 0. V by Lm1; :: thesis: verum